If you're going to a smaller airport in the middle of the US it can occasionally be cheaper to book two tickets with a break somewhere on the east coast (typically NYC, sometimes BOS, WAS or ATL), though this increases the risk of problems if one of your flights is delayed. However LON-LAX is a busy and competitive enough route that a single ticket all the way will pretty much always be cheaper. The single ticket may still involve changing somewhere, but in this case the airlines are obliged to help you in the event of delays.

Just put your destination and dates into Kayak.com and see what is cheapest.