diff --git a/docs/source/transforms.rst b/docs/source/transforms.rst
index 962e1f3769..01b1cb00bb 100644
--- a/docs/source/transforms.rst
+++ b/docs/source/transforms.rst
@@ -604,6 +604,12 @@ Utility
     :members:
     :special-members: __call__
 
+`RandLambda`
+""""""""""""
+.. autoclass:: RandLambda
+    :members:
+    :special-members: __call__
+
 `LabelToMask`
 """""""""""""
 .. autoclass:: LabelToMask
diff --git a/monai/transforms/__init__.py b/monai/transforms/__init__.py
index 45eecd266c..487a995e5e 100644
--- a/monai/transforms/__init__.py
+++ b/monai/transforms/__init__.py
@@ -323,6 +323,7 @@
     LabelToMask,
     Lambda,
     MapLabelValue,
+    RandLambda,
     RemoveRepeatedChannel,
     RepeatChannel,
     SimulateDelay,
diff --git a/monai/transforms/utility/array.py b/monai/transforms/utility/array.py
index 7f06f119c2..4e0141652f 100644
--- a/monai/transforms/utility/array.py
+++ b/monai/transforms/utility/array.py
@@ -23,7 +23,7 @@
 import torch
 
 from monai.config import DtypeLike, NdarrayTensor
-from monai.transforms.transform import Randomizable, Transform
+from monai.transforms.transform import Randomizable, RandomizableTransform, Transform
 from monai.transforms.utils import (
     convert_to_numpy,
     convert_to_tensor,
@@ -58,6 +58,7 @@
     "DataStats",
     "SimulateDelay",
     "Lambda",
+    "RandLambda",
     "LabelToMask",
     "FgBgToIndices",
     "ClassesToIndices",
@@ -617,6 +618,28 @@ def __call__(self, img: Union[np.ndarray, torch.Tensor], func: Optional[Callable
         raise ValueError("Incompatible values: func=None and self.func=None.")
 
 
+class RandLambda(Lambda, RandomizableTransform):
+    """
+    Randomizable version :py:class:`monai.transforms.Lambda`, the input `func` may contain random logic,
+    or randomly execute the function based on `prob`.
+
+    Args:
+        func: Lambda/function to be applied.
+        prob: probability of executing the random function, default to 1.0, with 100% probability to execute.
+
+    For more details, please check :py:class:`monai.transforms.Lambda`.
+
+    """
+
+    def __init__(self, func: Optional[Callable] = None, prob: float = 1.0) -> None:
+        Lambda.__init__(self=self, func=func)
+        RandomizableTransform.__init__(self=self, prob=prob)
+
+    def __call__(self, img: Union[np.ndarray, torch.Tensor], func: Optional[Callable] = None):
+        self.randomize(img)
+        return super().__call__(img=img, func=func) if self._do_transform else img
+
+
 class LabelToMask(Transform):
     """
     Convert labels to mask for other tasks. A typical usage is to convert segmentation labels
diff --git a/monai/transforms/utility/dictionary.py b/monai/transforms/utility/dictionary.py
index 6fa672e6c4..75be9685c4 100644
--- a/monai/transforms/utility/dictionary.py
+++ b/monai/transforms/utility/dictionary.py
@@ -24,8 +24,9 @@
 import torch
 
 from monai.config import DtypeLike, KeysCollection, NdarrayTensor
+from monai.data.utils import no_collation
 from monai.transforms.inverse import InvertibleTransform
-from monai.transforms.transform import MapTransform, Randomizable
+from monai.transforms.transform import MapTransform, Randomizable, RandomizableTransform
 from monai.transforms.utility.array import (
     AddChannel,
     AsChannelFirst,
@@ -833,7 +834,7 @@ def __call__(self, data):
         return d
 
 
-class Lambdad(MapTransform):
+class Lambdad(MapTransform, InvertibleTransform):
     """
     Dictionary-based wrapper of :py:class:`monai.transforms.Lambda`.
 
@@ -852,51 +853,110 @@ class Lambdad(MapTransform):
             See also: :py:class:`monai.transforms.compose.MapTransform`
         func: Lambda/function to be applied. It also can be a sequence of Callable,
             each element corresponds to a key in ``keys``.
+        inv_func: Lambda/function of inverse operation if want to invert transforms, default to `lambda x: x`.
+            It also can be a sequence of Callable, each element corresponds to a key in ``keys``.
         overwrite: whether to overwrite the original data in the input dictionary with lamdbda function output.
             default to True. it also can be a sequence of bool, each element corresponds to a key in ``keys``.
         allow_missing_keys: don't raise exception if key is missing.
+
+    Note: The inverse operation doesn't allow to define `extra_info` or access other information, such as the
+        image's original size. If need these complicated information, please write a new InvertibleTransform directly.
+
     """
 
     def __init__(
         self,
         keys: KeysCollection,
         func: Union[Sequence[Callable], Callable],
+        inv_func: Union[Sequence[Callable], Callable] = no_collation,
         overwrite: Union[Sequence[bool], bool] = True,
         allow_missing_keys: bool = False,
     ) -> None:
         super().__init__(keys, allow_missing_keys)
         self.func = ensure_tuple_rep(func, len(self.keys))
+        self.inv_func = ensure_tuple_rep(inv_func, len(self.keys))
         self.overwrite = ensure_tuple_rep(overwrite, len(self.keys))
         self._lambd = Lambda()
 
+    def _transform(self, data: Any, func: Callable):
+        return self._lambd(data, func=func)
+
     def __call__(self, data):
         d = dict(data)
         for key, func, overwrite in self.key_iterator(d, self.func, self.overwrite):
-            ret = self._lambd(d[key], func=func)
+            ret = self._transform(data=d[key], func=func)
+            if overwrite:
+                d[key] = ret
+            self.push_transform(d, key)
+        return d
+
+    def _inverse_transform(self, transform_info: Dict, data: Any, func: Callable):
+        return self._lambd(data, func=func)
+
+    def inverse(self, data):
+        d = deepcopy(dict(data))
+        for key, inv_func, overwrite in self.key_iterator(d, self.inv_func, self.overwrite):
+            transform = self.get_most_recent_transform(d, key)
+            ret = self._inverse_transform(transform_info=transform, data=d[key], func=inv_func)
             if overwrite:
                 d[key] = ret
+            self.pop_transform(d, key)
         return d
 
 
-class RandLambdad(Lambdad, Randomizable):
+class RandLambdad(Lambdad, RandomizableTransform):
     """
-    Randomizable version :py:class:`monai.transforms.Lambdad`, the input `func` contains random logic.
-    It's a randomizable transform so `CacheDataset` will not execute it and cache the results.
+    Randomizable version :py:class:`monai.transforms.Lambdad`, the input `func` may contain random logic,
+    or randomly execute the function based on `prob`. so `CacheDataset` will not execute it and cache the results.
 
     Args:
         keys: keys of the corresponding items to be transformed.
             See also: :py:class:`monai.transforms.compose.MapTransform`
         func: Lambda/function to be applied. It also can be a sequence of Callable,
             each element corresponds to a key in ``keys``.
+        inv_func: Lambda/function of inverse operation if want to invert transforms, default to `lambda x: x`.
+            It also can be a sequence of Callable, each element corresponds to a key in ``keys``.
         overwrite: whether to overwrite the original data in the input dictionary with lamdbda function output.
             default to True. it also can be a sequence of bool, each element corresponds to a key in ``keys``.
+        prob: probability of executing the random function, default to 1.0, with 100% probability to execute.
+            note that all the data specified by `keys` will share the same random probability to execute or not.
+        allow_missing_keys: don't raise exception if key is missing.
 
     For more details, please check :py:class:`monai.transforms.Lambdad`.
 
+    Note: The inverse operation doesn't allow to define `extra_info` or access other information, such as the
+        image's original size. If need these complicated information, please write a new InvertibleTransform directly.
+
     """
 
-    def randomize(self, data: Any) -> None:
-        pass
+    def __init__(
+        self,
+        keys: KeysCollection,
+        func: Union[Sequence[Callable], Callable],
+        inv_func: Union[Sequence[Callable], Callable] = no_collation,
+        overwrite: Union[Sequence[bool], bool] = True,
+        prob: float = 1.0,
+        allow_missing_keys: bool = False,
+    ) -> None:
+        Lambdad.__init__(
+            self=self,
+            keys=keys,
+            func=func,
+            inv_func=inv_func,
+            overwrite=overwrite,
+            allow_missing_keys=allow_missing_keys,
+        )
+        RandomizableTransform.__init__(self=self, prob=prob, do_transform=True)
+
+    def _transform(self, data: Any, func: Callable):
+        return self._lambd(data, func=func) if self._do_transform else data
+
+    def __call__(self, data):
+        self.randomize(data)
+        return super().__call__(data)
+
+    def _inverse_transform(self, transform_info: Dict, data: Any, func: Callable):
+        return self._lambd(data, func=func) if transform_info[InverseKeys.DO_TRANSFORM] else data
 
 
 class LabelToMaskd(MapTransform):
diff --git a/tests/test_inverse.py b/tests/test_inverse.py
index a1c171200f..f2470d47fd 100644
--- a/tests/test_inverse.py
+++ b/tests/test_inverse.py
@@ -35,6 +35,7 @@
     DivisiblePadd,
     Flipd,
     InvertibleTransform,
+    Lambdad,
     LoadImaged,
     Orientationd,
     RandAffined,
@@ -42,6 +43,7 @@
     RandCropByLabelClassesd,
     RandCropByPosNegLabeld,
     RandFlipd,
+    RandLambdad,
     Randomizable,
     RandRotate90d,
     RandRotated,
@@ -314,6 +316,16 @@
 
 TESTS.append(("Resized longest 3d", "3D", 5e-2, Resized(KEYS, 201, "longest", "trilinear", True)))
 
+TESTS.append(("Lambdad 2d", "2D", 5e-2, Lambdad(KEYS, func=lambda x: x + 5, inv_func=lambda x: x - 5, overwrite=True)))
+
+TESTS.append(
+    (
+        "RandLambdad 3d",
+        "3D",
+        5e-2,
+        RandLambdad(KEYS, func=lambda x: x * 10, inv_func=lambda x: x / 10, overwrite=True, prob=0.5),
+    )
+)
 
 TESTS.append(
     (
diff --git a/tests/test_rand_lambda.py b/tests/test_rand_lambda.py
new file mode 100644
index 0000000000..bf537883cf
--- /dev/null
+++ b/tests/test_rand_lambda.py
@@ -0,0 +1,53 @@
+# Copyright 2020 - 2021 MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import unittest
+
+import numpy as np
+
+from monai.transforms.transform import Randomizable
+from monai.transforms.utility.array import RandLambda
+
+
+class RandTest(Randomizable):
+    """
+    randomisable transform for testing.
+    """
+
+    def randomize(self, data=None):
+        self._a = self.R.random()
+
+    def __call__(self, data):
+        self.randomize()
+        return data + self._a
+
+
+class TestRandLambda(unittest.TestCase):
+    def test_rand_lambdad_identity(self):
+        img = np.zeros((10, 10))
+
+        test_func = RandTest()
+        test_func.set_random_state(seed=134)
+        expected = test_func(img)
+        test_func.set_random_state(seed=134)
+        ret = RandLambda(func=test_func)(img)
+        np.testing.assert_allclose(expected, ret)
+        ret = RandLambda(func=test_func, prob=0.0)(img)
+        np.testing.assert_allclose(img, ret)
+
+        trans = RandLambda(func=test_func, prob=0.5)
+        trans.set_random_state(seed=123)
+        ret = trans(img)
+        np.testing.assert_allclose(img, ret)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/tests/test_rand_lambdad.py b/tests/test_rand_lambdad.py
index a450b67413..0a127839b8 100644
--- a/tests/test_rand_lambdad.py
+++ b/tests/test_rand_lambdad.py
@@ -42,6 +42,15 @@ def test_rand_lambdad_identity(self):
         ret = RandLambdad(keys=["img", "prop"], func=test_func, overwrite=[True, False])(data)
         np.testing.assert_allclose(expected["img"], ret["img"])
         np.testing.assert_allclose(expected["prop"], ret["prop"])
+        ret = RandLambdad(keys=["img", "prop"], func=test_func, prob=0.0)(data)
+        np.testing.assert_allclose(data["img"], ret["img"])
+        np.testing.assert_allclose(data["prop"], ret["prop"])
+
+        trans = RandLambdad(keys=["img", "prop"], func=test_func, prob=0.5)
+        trans.set_random_state(seed=123)
+        ret = trans(data)
+        np.testing.assert_allclose(data["img"], ret["img"])
+        np.testing.assert_allclose(data["prop"], ret["prop"])
 
 
 if __name__ == "__main__":