Upon landing and pulling into a gate at T7, you'll be loaded onto a bus and taken all the way over to TBIT to clear immigration and customs. Once you make it through the madhouse, you'll have to either briskly walk or grab the shuttle over to T6, clear security, and get out to your connecting gate.

Earlier this week I flew LHR-LAX with checked luggage and made a 3:14 connecting flight, but it was definitely rushed and stressful. I'd suggest booking the 4:05, and if you happen to have extra time, pop into the RCC.