Yep, you can do it easily. It's called "checking in short" or being "short checked," according to my gate agent friends. (Once I was flying ORD-SFO-NRT-SIN, and I live in SFO; I didn't have my passport at ORD, so I was short-checked ORD-SFO and then ran for my passport before being checked in for SFO-NRT-SIN with my passport.)

In this case, simply ask at LHR only to be checked in as far as LAX.

Domestically (LGA-ORD-SFO, for example, if you don't want your ORD-SFO BP at LGA), you can:
- use online checkin, then call the Web Support number and be offloaded from the second segment
- check in with an agent and only be checked in for LGA-ORD
- check in with Mr. Easy Checkin and then find an agent, give them your ORD-SFO, and have it torn up and you offloaded from the flight

Times I've done this, I've had no questions asked.