A bit closer than I'd like but if that's the way AA originally ticketed it then you're still within MCT. If you miss the original flight because of IRROPS there are four flights after 4pm from LAX to LAS and AA will put you on the next flight out.
You will need to clear Immigration, collect and then recheck your bags. The flights from LHR should come in when the CBP station in T4 is open so you won't have to hoof it to TBIT and then back to T4 (unless you get a bus gate then you'll have to get back to T4). All of the CBP stations AA uses have a Bag Recheck right after you leave Customs so you don't need to drag your bags all the way to the normal baggage check. If things are close then AA will likely expedite you through TSA.
Hope this helps.