I am a US citizen and will be traveling in January to Israel. On my return, I might have a seven-and-a-half-hour layover at Heathrow T5. Would that be enough time to pass through His Majesty's Border Force, ride Her late Majesty's purple train (Elizabeth Line) into the city for lunch and return to the airport and clear security in time for my flight?
For an US citizen there is no problem with visa so you can just try it, keeping an eye on the time and abort when you see the time is not working in your favour.
Count on 30 to 90 minutes to get out of the airport, 20 to 40 minutes to reach Paddington on the Elizabeth line and a few more for wherever you want to go in the city center or about an hour on the Piccadilly line, less if you are happy with the first real pub near the airport, or about 20 to 30 minutes plus more money for the Heathrow express, and again about half an hour to an hour to return to the airport.
I would expect to need at least one hour for a lunch but you can get by with less, if you inform the pub when you sit down that you are in a hurry.
That should leave you plenty of time to return and get through all hoops you need to jump through, if you do not run into delays.
So if your incoming flight is late, you need the full 90 minutes to leave the airport and/or the train(s) you want to take is not running as planned, consider your timings.
There are pubs a few underground stops from the airport, for if you are outside but run out of time for the whole travel and there are parts of the airport which are build in pub style for food service, which is a fake that might work if all goes wrong.