Which airline London-LAX. Are you sure that it is LHR-LAX..?
If so, you will depart from T3 or T4 ... T4 has nice shops to kill some time.... 3 hours layover is not too bad....I guess you'll arrive at T1....and 9:35 London time is 10:35 MEZ (Berlin/Copenhagen), so, your flight isn't a 'red-eye-flight'
Have a nice trip ^