Do I have to go through customs, immigration during my Heathrow layover? I'm switching airlines. I arrive on American from the USA (US Citizen) and depart for Lisbon on TAP. I will have no checked luggage, just carryon. I'm planning on a 3 hour layover. What are the details and is 3 hours enough time??
Heathrow has airside shuttles connecting all of the terminals, so you should be able to transfer between international flights on any airlines without passing immigration (though you will pass an airside-to-airside security checkpoint). Follow the "Connecting Flights" signs and pick up your boarding pass at the appropriate transfer desk if you didn't already get one when checking in for the first leg.
Three hours ought to be plenty if your inbound flight arrives on time. If it doesn't, well, then it depends on how late it is. You'll really want to be on a single tickets such that the airlines will be obliged to rebook you in that case. Or at least, I don't think any possible savings from traveling on different tickets over a single one would be worth the risk to me.
(When traveling on different tickets, another question would be whether the first carrier will let you board the inbound leg without being sure you have the right documentation to enter the UK in case of a missed or canceled connection -- but with a US passport that shouldn't be a problem for you in any case).