diff --git a/exla/lib/exla/defn.ex b/exla/lib/exla/defn.ex
index fbf392862f..3a676b5942 100644
--- a/exla/lib/exla/defn.ex
+++ b/exla/lib/exla/defn.ex
@@ -546,21 +546,15 @@ defmodule EXLA.Defn do
 
   defp cached_recur_operator(
          :lu,
-         %T{data: %Expr{args: [{p_expr, l_expr, u_expr}, tensor, _opts]}},
-         state,
+         %T{
+           data: %Expr{args: [{p_expr, l_expr, u_expr}, %{type: {type_kind, _}} = tensor, _opts]}
+         },
+         %{client: %{platform: :host}} = state,
          cache
-       ) do
-    %{type: {p_type_kind, _}} = p_expr
-    %{type: {out_type_kind, _}} = l_expr
-
-    if state.client.platform != :host do
-      raise ArgumentError, "XLA does not currently support the LU operation on non-host devices"
-    end
-
-    if p_type_kind == :c or out_type_kind == :c do
-      raise ArgumentError, "XLA does not currently support the LU operation for complex inputs"
-    end
-
+       )
+       when type_kind != :c do
+    # We only want to accelerate the LU operation for real inputs on the host device.
+    # Otherwise, we use the default implementation in Nx.
     {tensor, cache} = recur_operator(tensor, state, cache) |> unwrap_single_tensor!()
 
     tensor =