You will have to clear immigration on arrival then pick up your checked bags and go through customs. When you come out of customs you’ll see all the people waiting to greet people. Go to the far right and there is an area for connecting flights where you can recheck your bag and clear security from there. Not sure if British has agents there or not though. If they don’t you’ll need to walk to the other side of the terminal to take the elevator up to the ticketing area and check your bags at the British airways counter. Timing is tight and immigration lines at LAX can be long so don’t waste time. If you have Global Entry it will be significantly faster. Since it’s one one ticket you should be protected if you misconnect. But it may involve an extra stop somewhere or a different carrier.