testing before flying back to the US

I can't help you about Heathrow, but the US requirement is not 24 hours but "no more than one day before you travel by air into the US." So if you're flying nonstop from LHR to a US airport on Friday, your test sample must have been given on Thursday or Friday. A little more flexibility. It could be Thursday morning for a Friday evening flight. The airline will look at your documentation at check-in, and if it's negative you're good to fly.

The website says results within 30 minutes. If taking it at Heathrow, ensure you schedule it at your departure terminal. Check to see if the Boots in Liss tests. Many do.

The US currently accepts proctored self-tests, such as the Abbott BinaxNOW, but you should check your airline's policy to be sure. You could order a couple of the tests and take them with you in case you run into difficulties scheduling an in-person test.

try Boots in Portsmouth, Winchester, Guildford

https://www.boots.com/covid-19-testing

This is all helpful, thanks! Its especially helpful to know that its not 24 hours but 1 day. That's less pressure.

I had looked into Boots but it looks like most of the sites in Hampshire have results in 24-48 hours, which makes me a little nervous. I'm thinking the best thing might be to do a test at the airport with the shorter wait time.

A lot of the options at Heathrow are lateral flow tests, and my understanding is that the US does not accept lateral flow tests - they have to be a PCR or a NAAT antigen tests (at least this is what was required last fall when I returned to the US from Europe), but since there are so many lft options at Heathrow, I'm wondering if I'm wrong about this?

You want the lateral flow / rapid antigen test.

I'm surprised that Boots are taking so long for a LFT. It is usually done in less than half an hour.

Currently (and at all times when the US has been requiring a negative test for entry) a lateral flow test is perfectly acceptable for entry to the United States. Just did it a couple weeks ago, and did it multiple times over the summer and autumn. No need for the pricier PCR. I am not aware of any testing provider that takes more than a few hours to turn around a lateral flow test.

Here is the link to the CDC webpage with information on what tests are acceptable for a return to the US which include:

"You must be tested with a viral test to look for current infection – these include an antigen test or a nucleic acid amplification test (NAAT).

Phrases indicating a test is an antigen test could include, but not are not limited to:

Rapid antigen test
Viral antigen test
Also, could be noted as Antigen Chromatographic Digital Immunoassay, Antigen Chemiluminescence Immunoassay, or Antigen Lateral Flow Fluorescence

Examples of available NAATs for SARS-CoV-2 include but are not restricted to:

Reverse transcription polymerase chain reaction (RT-PCR)
Isothermal amplification including:
Nicking endonuclease amplification reaction (NEAR)
Transcription mediated amplification (TMA)
Loop-mediated isothermal amplification (LAMP)
Helicase-dependent amplification (HDA)
Clustered regularly interspaced short palindromic repeats (CRISPR)
Strand displacement amplification (SDA)

The test used must be authorized for use by the relevant national authority for the detection of SARS-CoV-2 in the country where the test is administered."

https://www.cdc.gov/coronavirus/2019-ncov/travelers/testing-international-air-travelers.html