diff --git a/mangum/adapter.py b/mangum/adapter.py
index 60670e4..ff41519 100644
--- a/mangum/adapter.py
+++ b/mangum/adapter.py
@@ -76,7 +76,7 @@ def __call__(self, event: LambdaEvent, context: LambdaContext) -> dict:
             if self.lifespan in ("auto", "on"):
                 lifespan_cycle = LifespanCycle(self.app, self.lifespan)
                 stack.enter_context(lifespan_cycle)
-                scope |= {"state": lifespan_cycle.lifespan_state.copy()}
+                scope.update({"state": lifespan_cycle.lifespan_state.copy()})
 
             http_cycle = HTTPCycle(scope, handler.body)
             http_response = http_cycle(self.app)
diff --git a/mangum/protocols/http.py b/mangum/protocols/http.py
index fc95787..6ab6b37 100644
--- a/mangum/protocols/http.py
+++ b/mangum/protocols/http.py
@@ -3,8 +3,8 @@
 import logging
 from io import BytesIO
 
-from mangum.types import ASGI, Message, Scope, Response
 from mangum.exceptions import UnexpectedMessage
+from mangum.types import ASGI, Message, Response, Scope
 
 
 class HTTPCycleState(enum.Enum):
@@ -82,11 +82,17 @@ async def receive(self) -> Message:
         return await self.app_queue.get()  # pragma: no cover
 
     async def send(self, message: Message) -> None:
-        if self.state is HTTPCycleState.REQUEST and message["type"] == "http.response.start":
+        if (
+            self.state is HTTPCycleState.REQUEST
+            and message["type"] == "http.response.start"
+        ):
             self.status = message["status"]
             self.headers = message.get("headers", [])
             self.state = HTTPCycleState.RESPONSE
-        elif self.state is HTTPCycleState.RESPONSE and message["type"] == "http.response.body":
+        elif (
+            self.state is HTTPCycleState.RESPONSE
+            and message["type"] == "http.response.body"
+        ):
             body = message.get("body", b"")
             more_body = message.get("more_body", False)
             self.buffer.write(body)
diff --git a/mangum/protocols/lifespan.py b/mangum/protocols/lifespan.py
index 193ebcc..8d7fe05 100644
--- a/mangum/protocols/lifespan.py
+++ b/mangum/protocols/lifespan.py
@@ -2,10 +2,10 @@
 import enum
 import logging
 from types import TracebackType
-from typing import Optional, Type, Any
+from typing import Any, Dict, Optional, Type
 
+from mangum.exceptions import LifespanFailure, LifespanUnsupported, UnexpectedMessage
 from mangum.types import ASGI, LifespanMode, Message
-from mangum.exceptions import LifespanUnsupported, LifespanFailure, UnexpectedMessage
 
 
 class LifespanCycleState(enum.Enum):
@@ -62,7 +62,7 @@ def __init__(self, app: ASGI, lifespan: LifespanMode) -> None:
         self.startup_event: asyncio.Event = asyncio.Event()
         self.shutdown_event: asyncio.Event = asyncio.Event()
         self.logger = logging.getLogger("mangum.lifespan")
-        self.lifespan_state: dict[str, Any] = {}
+        self.lifespan_state: Dict[str, Any] = {}
 
     def __enter__(self) -> None:
         """Runs the event loop for application startup."""
diff --git a/tests/test_lifespan.py b/tests/test_lifespan.py
index ac09aa4..12a98ef 100644
--- a/tests/test_lifespan.py
+++ b/tests/test_lifespan.py
@@ -1,15 +1,13 @@
 import logging
 
 import pytest
-
+from quart import Quart
 from starlette.applications import Starlette
 from starlette.responses import PlainTextResponse
 
 from mangum import Mangum
 from mangum.exceptions import LifespanFailure
 
-from quart import Quart
-
 
 @pytest.mark.parametrize(
     "mock_aws_api_gateway_event,lifespan",
@@ -211,6 +209,58 @@ async def app(scope, receive, send):
         handler(mock_aws_api_gateway_event, {})
 
 
+@pytest.mark.parametrize(
+    "mock_aws_api_gateway_event,lifespan_state,lifespan",
+    [
+        (["GET", None, None], {"test_key": "test_value"}, "auto"),
+        (["GET", None, None], {"test_key": "test_value"}, "on"),
+    ],
+    indirect=["mock_aws_api_gateway_event"],
+)
+def test_lifespan_state(mock_aws_api_gateway_event, lifespan_state, lifespan) -> None:
+    startup_complete = False
+    shutdown_complete = False
+
+    async def app(scope, receive, send):
+        nonlocal startup_complete, shutdown_complete
+
+        if scope["type"] == "lifespan":
+            while True:
+                message = await receive()
+                if message["type"] == "lifespan.startup":
+                    scope["state"].update(lifespan_state)
+                    await send({"type": "lifespan.startup.complete"})
+                    startup_complete = True
+                elif message["type"] == "lifespan.shutdown":
+                    await send({"type": "lifespan.shutdown.complete"})
+                    shutdown_complete = True
+                    return
+
+        if scope["type"] == "http":
+            assert lifespan_state.items() <= scope["state"].items()
+            await send(
+                {
+                    "type": "http.response.start",
+                    "status": 200,
+                    "headers": [[b"content-type", b"text/plain; charset=utf-8"]],
+                }
+            )
+            await send({"type": "http.response.body", "body": b"Hello, world!"})
+
+    handler = Mangum(app, lifespan=lifespan)
+    response = handler(mock_aws_api_gateway_event, {})
+
+    assert startup_complete
+    assert shutdown_complete
+    assert response == {
+        "statusCode": 200,
+        "isBase64Encoded": False,
+        "headers": {"content-type": "text/plain; charset=utf-8"},
+        "multiValueHeaders": {},
+        "body": "Hello, world!",
+    }
+
+
 @pytest.mark.parametrize("mock_aws_api_gateway_event", [["GET", None, None]], indirect=True)
 def test_starlette_lifespan(mock_aws_api_gateway_event) -> None:
     startup_complete = False