diff --git a/src/lightning/pytorch/core/module.py b/src/lightning/pytorch/core/module.py
index bae7f876c8211..355f49b6c3cdf 100644
--- a/src/lightning/pytorch/core/module.py
+++ b/src/lightning/pytorch/core/module.py
@@ -16,6 +16,7 @@
 import copy
 import logging
 import numbers
+import warnings
 import weakref
 from collections.abc import Generator, Mapping, Sequence
 from contextlib import contextmanager, nullcontext
@@ -1329,10 +1330,26 @@ def lr_scheduler_step(self, scheduler, metric):
                 scheduler.step(epoch=self.current_epoch)
 
         """
-        if metric is None:
-            scheduler.step()  # type: ignore[call-arg]
-        else:
-            scheduler.step(metric)
+        with warnings.catch_warnings(record=True) as caught:
+            warnings.simplefilter("always")
+
+            if metric is None:
+                scheduler.step()  # type: ignore[call-arg]
+            else:
+                scheduler.step(metric)
+
+        for w in caught:
+            msg = str(w.message)
+
+            if "lr_scheduler.step()" in msg and "optimizer.step()" in msg:
+                msg = (
+                    f"{msg} Lightning note: When training in mixed/half precision "
+                    "(e.g., 16-bit), an overflow on the first iteration can skip the "
+                    "optimizer step; the scheduler then runs before any optimizer "
+                    "step, which surfaces this warning."
+                )
+
+            rank_zero_warn(msg, category=w.category, stacklevel=2)
 
     def optimizer_step(
         self,
diff --git a/tests/tests_pytorch/core/test_lightning_module.py b/tests/tests_pytorch/core/test_lightning_module.py
index c33488a4f2626..3ecd0a7a1b1e8 100644
--- a/tests/tests_pytorch/core/test_lightning_module.py
+++ b/tests/tests_pytorch/core/test_lightning_module.py
@@ -446,6 +446,45 @@ def test_lightning_module_scriptable():
     torch.jit.script(model)
 
 
+@RunIf(min_cuda_gpus=1)
+def test_lr_scheduler_step_warning_message(tmp_path):
+    class MinimalSchedulerModel(BoringModel):
+        def training_step(self, batch, batch_idx):
+            loss = self.step(batch)
+            if batch_idx == 0:
+                loss = loss * torch.tensor(float("nan"), device=self.device)
+            return loss
+
+        def configure_optimizers(self):
+            optimizer = torch.optim.SGD(self.parameters(), lr=0.1)
+            scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=1)
+            return {"optimizer": optimizer, "lr_scheduler": {"scheduler": scheduler, "interval": "step"}}
+
+    trainer = Trainer(
+        default_root_dir=tmp_path,
+        accelerator="gpu",
+        devices=1,
+        precision="16-mixed",
+        max_steps=2,
+        limit_train_batches=2,
+        limit_val_batches=0,
+        logger=False,
+        enable_checkpointing=False,
+        enable_model_summary=False,
+        enable_progress_bar=False,
+    )
+
+    model = MinimalSchedulerModel()
+
+    warning_match = (
+        r"lr_scheduler\.step\(\).*optimizer\.step\(\).*"
+        r"Lightning note: When training in mixed/half precision \(e\.g\., 16-bit\)"
+    )
+
+    with pytest.warns(UserWarning, match=warning_match):
+        trainer.fit(model)
+
+
 def test_trainer_reference_recursively():
     ensemble = LightningModule()
     inner = LightningModule()