Passport Control & Customs Coming from Switzerland

Is it foolish to book a flight arriving at LHR that 45 minutes before the scheduled departure of the flight to the US (which is a Delta flight)?

yes this is foolish because the first flight may be delayed causing you to miss the other

That's too tight of a connection. At minimum you will probably need to go through a security screening.

Hopefully you can re-book one of your flights, for either an earlier arrival at LHR or later departure from LHR. Otherwise I strongly suspect, that you will be buying a new ticket, because you missed your US bound flight from LHR.

Do you have to change terminals? If so your odds of success are 0.00000000000001%

I assume I will be going through immigration and customs at LHR, correct?

not if you go through flight connections and do not cross the UK border you won't

You've been given very good advice.

Go to Heathrow Flight Connections, plug in your flight connections and it will give you step by step instructions on what you have to do to change from one flight to another.

The only airlines that fly from Geneva to Heathrow are British Airways and Swiss International which arrive at Terminals 5 and 2 respectively. Delta is out of Terminal 3.

Forty five minutes is not close enough. I believe 75 minutes is the absolute minimum time suggested.

Plus, they do not allow boarding right up until departure, they may close boarding 15 minutes, up to a half hour before "departure", you need to be at the gate well before that.

45 minutes is just madness. It could take 20 mins from touchdown to door open at the arrival gate. I wouldn't be comfortable with anything less than a three hour gap between flights, and that's when it's a true connection one one ticket. Remember, on an unprotected connection if you miss the 2nd flight you'll have to buy a full-price ticket for the next available flight.

Thanks everyone for the responses. I need to get an earlier flight into LHR!

2nd: Is it foolish to book a flight arriving at LHR that 45 minutes before the scheduled departure of the flight to the US (which is a Delta flight)?

No. It's insane.

Changing terminals on separate tickets I wouldn't do it with less than 2 hours, probably 3. But that's just me because I don't want to rush. Even just traveling domestically in the US I won't do connections less than 90 minutes.

It's utterly insane, change the GVA to LHR flight immediately to arrive the day before, even if you have to eat a night of a prepaid hotel .
You can pay off the national debt with the cost of a walk up ticket from LHR back to wherever you're going in the USA, there is no chance you're making a flight with a non protected 45 minute connection through LHR.