diff --git a/narwhals/_spark_like/namespace.py b/narwhals/_spark_like/namespace.py
index b7e3bfb78..87963c417 100644
--- a/narwhals/_spark_like/namespace.py
+++ b/narwhals/_spark_like/namespace.py
@@ -16,6 +16,7 @@
 from narwhals._spark_like.selectors import SparkLikeSelectorNamespace
 from narwhals._spark_like.utils import ExprKind
 from narwhals._spark_like.utils import n_ary_operation_expr_kind
+from narwhals._spark_like.utils import narwhals_to_native_dtype
 from narwhals.typing import CompliantNamespace
 
 if TYPE_CHECKING:
@@ -80,12 +81,15 @@ def nth(self: Self, *column_indices: int) -> SparkLikeExpr:
         )
 
     def lit(self: Self, value: object, dtype: DType | None) -> SparkLikeExpr:
-        if dtype is not None:
-            msg = "todo"
-            raise NotImplementedError(msg)
-
         def _lit(df: SparkLikeLazyFrame) -> list[Column]:
-            return [df._F.lit(value)]
+            column = df._F.lit(value)
+            if dtype:
+                native_dtype = narwhals_to_native_dtype(
+                    dtype, version=self._version, spark_types=df._native_dtypes
+                )
+                column = column.cast(native_dtype)
+
+            return [column]
 
         return SparkLikeExpr(
             call=_lit,
diff --git a/narwhals/_spark_like/utils.py b/narwhals/_spark_like/utils.py
index 3a728d5c5..7ef7f6b01 100644
--- a/narwhals/_spark_like/utils.py
+++ b/narwhals/_spark_like/utils.py
@@ -65,8 +65,10 @@ def native_to_narwhals_dtype(
         return dtypes.Boolean()
     if isinstance(dtype, spark_types.DateType):
         return dtypes.Date()
-    if isinstance(dtype, (spark_types.TimestampType, spark_types.TimestampNTZType)):
+    if isinstance(dtype, spark_types.TimestampNTZType):
         return dtypes.Datetime()
+    if isinstance(dtype, spark_types.TimestampType):
+        return dtypes.Datetime(time_zone="UTC")
     if isinstance(dtype, spark_types.DecimalType):  # pragma: no cover
         # TODO(unassigned): cover this in dtypes_test.py
         return dtypes.Decimal()
@@ -100,9 +102,16 @@ def narwhals_to_native_dtype(
         return spark_types.StringType()
     if isinstance_or_issubclass(dtype, dtypes.Boolean):
         return spark_types.BooleanType()
-    if isinstance_or_issubclass(dtype, (dtypes.Date, dtypes.Datetime)):
-        msg = "Converting to Date or Datetime dtype is not supported yet"
-        raise NotImplementedError(msg)
+    if isinstance_or_issubclass(dtype, dtypes.Date):
+        return spark_types.DateType()
+    if isinstance_or_issubclass(dtype, dtypes.Datetime):
+        dt_time_zone = getattr(dtype, "time_zone", None)
+        if dt_time_zone is None:
+            return spark_types.TimestampNTZType()
+        if dt_time_zone != "UTC":  # pragma: no cover
+            msg = f"Only UTC time zone is supported for PySpark, got: {dt_time_zone}"
+            raise ValueError(msg)
+        return spark_types.TimestampType()
     if isinstance_or_issubclass(dtype, dtypes.List):  # pragma: no cover
         inner = narwhals_to_native_dtype(
             dtype.inner,  # type: ignore[union-attr]
diff --git a/tests/expr_and_series/lit_test.py b/tests/expr_and_series/lit_test.py
index 900592766..6907b00c7 100644
--- a/tests/expr_and_series/lit_test.py
+++ b/tests/expr_and_series/lit_test.py
@@ -22,13 +22,10 @@
     [(None, [2, 2, 2]), (nw.String, ["2", "2", "2"]), (nw.Float32, [2.0, 2.0, 2.0])],
 )
 def test_lit(
-    request: pytest.FixtureRequest,
     constructor: Constructor,
     dtype: DType | None,
     expected_lit: list[Any],
 ) -> None:
-    if "pyspark" in str(constructor) and dtype is not None:
-        request.applymarker(pytest.mark.xfail)
     data = {"a": [1, 3, 2], "b": [4, 4, 6], "z": [7.0, 8.0, 9.0]}
     df_raw = constructor(data)
     df = nw.from_native(df_raw).lazy()
@@ -83,6 +80,7 @@ def test_lit_out_name(constructor: Constructor) -> None:
         ("right_scalar", nw.col("a") + 1, [2, 4, 3]),
         ("left_scalar_with_agg", 1 + nw.col("a").mean(), [3]),
         ("right_scalar_with_agg", nw.col("a").mean() - 1, [1]),
+        ("lit_compare", nw.col("a") == nw.lit(3), [False, True, False]),
     ],
 )
 def test_lit_operation_in_select(
@@ -130,7 +128,7 @@ def test_lit_operation_in_with_columns(
 
 @pytest.mark.skipif(PANDAS_VERSION < (1, 5), reason="too old for pyarrow")
 def test_date_lit(constructor: Constructor, request: pytest.FixtureRequest) -> None:
-    if "dask" in str(constructor) or "pyspark" in str(constructor):
+    if "dask" in str(constructor):
         # https://github.com/dask/dask/issues/11637
         request.applymarker(pytest.mark.xfail)
     df = nw.from_native(constructor({"a": [1]}))