diff --git a/bayesflow/data_adapters/transforms/lambda_transform.py b/bayesflow/data_adapters/transforms/lambda_transform.py
index 5b1bf2395..a2552069d 100644
--- a/bayesflow/data_adapters/transforms/lambda_transform.py
+++ b/bayesflow/data_adapters/transforms/lambda_transform.py
@@ -8,6 +8,14 @@
 
 @serializable(package="bayesflow.data_adapters")
 class LambdaTransform(Transform):
+    """
+    Transforms a parameter using a pair of forward and inverse functions.
+
+    Important note: This class is only serializable if the forward and inverse functions are serializable.
+    This most likely means you will have to pass the scope that the forward and inverse functions are contained in
+    to the `custom_objects` argument of the `deserialize` function when deserializing this class.
+    """
+
     def __init__(self, parameter_name: str, forward: callable, inverse: callable):
         super().__init__(parameter_name)
 
@@ -16,11 +24,15 @@ def __init__(self, parameter_name: str, forward: callable, inverse: callable):
 
     @classmethod
     def from_config(cls, config: dict, custom_objects=None) -> "LambdaTransform":
-        return cls(config["parameter_name"], deserialize(config["forward"]), deserialize(config["inverse"]))
+        return cls(
+            deserialize(config["parameter_name"], custom_objects),
+            deserialize(config["forward"], custom_objects),
+            deserialize(config["inverse"], custom_objects),
+        )
 
     def get_config(self) -> dict:
         return {
-            "parameter_name": self.parameter_name,
+            "parameter_name": serialize(self.parameter_name),
             "forward": serialize(self.forward),
             "inverse": serialize(self.inverse),
         }
diff --git a/tests/test_data_adapters/conftest.py b/tests/test_data_adapters/conftest.py
index ec7365cb5..0cdcb0e93 100644
--- a/tests/test_data_adapters/conftest.py
+++ b/tests/test_data_adapters/conftest.py
@@ -2,13 +2,32 @@
 import pytest
 
 
+def forward_transform(x):
+    return x + 1
+
+
+def inverse_transform(x):
+    return x - 1
+
+
+@pytest.fixture()
+def custom_objects():
+    return globals() | np.__dict__
+
+
 @pytest.fixture()
 def data_adapter():
     from bayesflow.data_adapters import ConcatenateKeysDataAdapter
+    from bayesflow.data_adapters.transforms import LambdaTransform, Normalize
 
     return ConcatenateKeysDataAdapter(
         x=["x1", "x2"],
         y=["y1", "y2"],
+        transforms=[
+            Normalize("x1", mean=np.array([0.0]), std=np.array([1.0])),
+            # use a lambda transform with global functions
+            LambdaTransform("x2", forward_transform, inverse_transform),
+        ],
     )
 
 
diff --git a/tests/test_data_adapters/test_data_adapters.py b/tests/test_data_adapters/test_data_adapters.py
index 34cb224f0..f5ff155d9 100644
--- a/tests/test_data_adapters/test_data_adapters.py
+++ b/tests/test_data_adapters/test_data_adapters.py
@@ -14,9 +14,9 @@ def test_cycle_consistency(data_adapter, random_data):
         assert keras.ops.all(keras.ops.isclose(value, deprocessed[key]))
 
 
-def test_serialize_deserialize(data_adapter):
+def test_serialize_deserialize(data_adapter, custom_objects):
     serialized = serialize(data_adapter)
-    deserialized = deserialize(serialized)
+    deserialized = deserialize(serialized, custom_objects)
     reserialized = serialize(deserialized)
 
     assert reserialized == serialized