diff --git a/narwhals/dataframe.py b/narwhals/dataframe.py
index 0fb1acecb..b055fed12 100644
--- a/narwhals/dataframe.py
+++ b/narwhals/dataframe.py
@@ -16,6 +16,7 @@
 
 from narwhals.dependencies import get_polars
 from narwhals.dependencies import is_numpy_array
+from narwhals.exceptions import OrderDependentExprError
 from narwhals.schema import Schema
 from narwhals.translate import to_native
 from narwhals.utils import find_stacklevel
@@ -3646,7 +3647,7 @@ def _extract_compliant(self, arg: Any) -> Any:
                     "  In a future version of Narwhals, a `order_by` argument will be added and \n"
                     "  they will be supported."
                 )
-                raise TypeError(msg)
+                raise OrderDependentExprError(msg)
             return arg._to_compliant_expr(self.__narwhals_namespace__())
         if get_polars() is not None and "polars" in str(type(arg)):  # pragma: no cover
             msg = (
diff --git a/narwhals/exceptions.py b/narwhals/exceptions.py
index 61447e54f..9b05e3ba8 100644
--- a/narwhals/exceptions.py
+++ b/narwhals/exceptions.py
@@ -83,6 +83,14 @@ def from_expr_name(cls, expr_name: str) -> AnonymousExprError:
         return AnonymousExprError(message)
 
 
+class OrderDependentExprError(ValueError):
+    """Exception raised when trying to use an order-dependent expressions with LazyFrames."""
+
+    def __init__(self, message: str) -> None:
+        self.message = message
+        super().__init__(self.message)
+
+
 class UnsupportedDTypeError(ValueError):
     """Exception raised when trying to convert to a DType which is not supported by the given backend."""