How to trigger lifespan startup and shutdown while testing FastAPI app?

Being very new to FastAPI I am strugling to test slightly more difficult code than I saw in the tutorial. I use fastapi_cache module and Redis like this:

from fastapi import Depends, FastAPI, Query, Request
from fastapi_cache.backends.redis import CACHE_KEY, RedisCacheBackend
from fastapi_cache import caches, close_caches

app = FastAPI()

def redis_cache():
    return caches.get(CACHE_KEY)    

@app.get('/cache')
async def test(
    cache: RedisCacheBackend = Depends(redis_cache),
    n: int = Query(
        ..., 
        gt=-1
    )
):  
    # code that uses redis cache

@app.on_event('startup')
async def on_startup() -> None:
    rc = RedisCacheBackend('redis://redis')
    caches.set(CACHE_KEY, rc)

@app.on_event('shutdown')
async def on_shutdown() -> None:
    await close_caches()

test_main.py looks like this:

import pytest
from httpx import AsyncClient
from .main import app

@pytest.mark.asyncio
async def test_cache():
    async with AsyncClient(app=app, base_url="http://test") as ac:
        response = await ac.get("/cache?n=150")

When I run pytest, it sets cache variable to None and test fails. I think I understand why the code is not working. But how do I fix it to test my caching properly?