Yes, you don't actually want the First Class Lounge at Heathrow. That is a little scam by BA to keep out riff-raff. You want The Concorde Room.

As you're American, it will almost certainly be the most amazing airport lounge experience you have ever seen :-). We just see it as a very civilised place to get a premium drink and a full restaurant meal before the plane goes. I recommend the Bollinger Rose.

If you want one of the free spa treatments, ring You First and pre-book otherwise you won't get.