diff --git a/starlette/routing.py b/starlette/routing.py
index cef1ef484..792b6abaa 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -541,29 +541,47 @@ async def lifespan(self, scope: Scope, receive: Receive, send: Send) -> None:
         Handle ASGI lifespan messages, which allows us to manage application
         startup and shutdown events.
         """
-        first = True
         app = scope.get("app")
         await receive()
+
+        async def as_aiter(gen: typing.Generator) -> typing.AsyncGenerator:
+            for val in gen:
+                yield val
+
+        lifespan_gen = (
+            self.lifespan_context(app)
+            if inspect.isasyncgenfunction(self.lifespan_context)
+            else as_aiter(self.lifespan_context(app))  # type: ignore
+        )
+
+        await self._lifespan_iter(lifespan_gen, receive, send)
+
+    async def _lifespan_iter(
+        self, gen: typing.AsyncGenerator, receive: Receive, send: Send
+    ) -> None:
         try:
-            if inspect.isasyncgenfunction(self.lifespan_context):
-                async for item in self.lifespan_context(app):
-                    assert first, "Lifespan context yielded multiple times."
-                    first = False
-                    await send({"type": "lifespan.startup.complete"})
-                    await receive()
-            else:
-                for item in self.lifespan_context(app):  # type: ignore
-                    assert first, "Lifespan context yielded multiple times."
-                    first = False
-                    await send({"type": "lifespan.startup.complete"})
-                    await receive()
-        except BaseException:
-            if first:
-                exc_text = traceback.format_exc()
-                await send({"type": "lifespan.startup.failed", "message": exc_text})
+            await gen.asend(None)
+        except StopAsyncIteration:
+            raise RuntimeError("Lifespan context never yielded.")
+        except Exception:
+            exc_text = traceback.format_exc()
+            await send({"type": "lifespan.startup.failed", "message": exc_text})
             raise
         else:
+            await send({"type": "lifespan.startup.complete"})
+            await receive()
+
+        try:
+            await gen.asend(None)
+        except StopAsyncIteration:
             await send({"type": "lifespan.shutdown.complete"})
+        except Exception:
+            exc_text = traceback.format_exc()
+            await send({"type": "lifespan.shutdown.failed", "message": exc_text})
+            raise
+        else:
+            await gen.aclose()
+            raise RuntimeError("Lifespan context yielded multiple times.")
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         """
diff --git a/starlette/testclient.py b/starlette/testclient.py
index c1c0fe165..54ce5fe5a 100644
--- a/starlette/testclient.py
+++ b/starlette/testclient.py
@@ -528,4 +528,11 @@ async def wait_shutdown(self) -> None:
             message = await self.stream_send.receive()
             if message is None:
                 self.task.result()
-            assert message["type"] == "lifespan.shutdown.complete"
+            assert message["type"] in (
+                "lifespan.shutdown.complete",
+                "lifespan.shutdown.failed",
+            )
+            if message["type"] == "lifespan.shutdown.failed":
+                message = await self.stream_send.receive()
+                if message is None:
+                    self.task.result()
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 1d8eb8d95..d418ea389 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -528,6 +528,31 @@ async def run_shutdown():
     assert shutdown_complete
 
 
+def test_lifespan_context_async():
+    startup_complete = False
+    shutdown_complete = False
+
+    async def hello_world(request):
+        return PlainTextResponse("hello, world")
+
+    async def lifespan(app):
+        nonlocal startup_complete, shutdown_complete
+        startup_complete = True
+        yield
+        shutdown_complete = True
+
+    app = Router(lifespan=lifespan, routes=[Route("/", hello_world)])
+
+    assert not startup_complete
+    assert not shutdown_complete
+    with TestClient(app) as client:
+        assert startup_complete
+        assert not shutdown_complete
+        client.get("/")
+    assert startup_complete
+    assert shutdown_complete
+
+
 def test_lifespan_sync():
     startup_complete = False
     shutdown_complete = False
@@ -559,6 +584,31 @@ def run_shutdown():
     assert shutdown_complete
 
 
+def test_lifespan_context_sync():
+    startup_complete = False
+    shutdown_complete = False
+
+    def hello_world(request):
+        return PlainTextResponse("hello, world")
+
+    def lifespan(app):
+        nonlocal startup_complete, shutdown_complete
+        startup_complete = True
+        yield
+        shutdown_complete = True
+
+    app = Router(lifespan=lifespan, routes=[Route("/", hello_world)])
+
+    assert not startup_complete
+    assert not shutdown_complete
+    with TestClient(app) as client:
+        assert startup_complete
+        assert not shutdown_complete
+        client.get("/")
+    assert startup_complete
+    assert shutdown_complete
+
+
 def test_raise_on_startup():
     def run_startup():
         raise RuntimeError()
@@ -585,11 +635,61 @@ def test_raise_on_shutdown():
     def run_shutdown():
         raise RuntimeError()
 
-    app = Router(on_shutdown=[run_shutdown])
+    router = Router(on_shutdown=[run_shutdown])
 
+    async def app(scope, receive, send):
+        async def _send(message):
+            nonlocal shutdown_failed
+            if message["type"] == "lifespan.shutdown.failed":
+                shutdown_failed = True
+            return await send(message)
+
+        await router(scope, receive, _send)
+
+    shutdown_failed = False
     with pytest.raises(RuntimeError):
         with TestClient(app):
             pass  # pragma: nocover
+    assert shutdown_failed
+
+
+def test_lifespan_yield_too_many():
+    startup_complete = False
+    shutdown_complete = False
+
+    async def hello_world(request):
+        return PlainTextResponse("hello, world")
+
+    async def yield_too_many(app):
+        nonlocal startup_complete, shutdown_complete
+        startup_complete = True
+        yield
+        yield
+        shutdown_complete = True  # pragma: nocover
+
+    app = Router(lifespan=yield_too_many, routes=[Route("/", hello_world)])
+
+    assert not startup_complete
+    assert not shutdown_complete
+    with pytest.raises(RuntimeError, match="yielded multiple times"):
+        with TestClient(app) as client:
+            assert startup_complete
+            assert not shutdown_complete
+            client.get("/")
+
+    assert startup_complete
+    assert not shutdown_complete
+
+
+def test_lifespan_yield_too_few():
+    async def yield_too_few(app):
+        for _ in []:
+            yield _  # pragma: nocover
+
+    app = Router(lifespan=yield_too_few)
+    with pytest.raises(RuntimeError, match="never yielded"):
+        with TestClient(app):
+            pass  # pragma: nocover
 
 
 class AsyncEndpointClassMethod: