What time is the LAX->LHR flight? 50 minutes is tight but not especially bad for that kind of transfer as long as everything is on time. On most days in the summer there are 6 or so LAX->LHR flights on other airlines after the last United LAX->LHR that United can interline you onto if you do have difficulty, although you may have to push a bit to be reaccommodated onto another airline. It may be worth looking at other potential connecting cities though--since it's a schedule change United will be pretty accommodating.