Most of the current LFTs (Rapid Antigen Tests, RAT) look for antigens - fragments of the virus (from nasopharyngeal swabs). Fragments of the virus will continue to circulate in your system for days, even up to a few weeks after infection. Some of the earlier LFTs identified antibodies to various virus structural proteins (from drops of blood). Neither necessarily correlates with infectiousness, though can be used as proxies to varying and limited degrees (the antibody ones less so).
If you are immunocompetent AND have had the full set of vaccinations (the original three jabs, aka two-dose primary series plus one 'booster', where at least one interval in that series was a good six months) then once you are at least 5 days past the first positive RAT LFT you are probably not infectious to other, fully vaccinated, immunocompetents (though give it 7 or even 10 days to be thoroughly sure).
However if you care for, work, live with, or otherwise associate with clinically vulnerable/immunodysfunctional persons, then you should consider allowing for at least 10 days to pass and/or wear a proper, fitted face mask (FFP2/N95, or better) around them. Better: 14 days.
Current
CDC guidance provides more details.