I've been in a similar situation a couple of times. Positive LFT (but a faint line that some people would possibly ignore) followed up by negative PCR (and a negative LFT later the same day). 3 months later exactly the same thing happened again - so even if I did have Covid one of those times it seems at least one of them must have been a false positive (albeit the internet says this is a 1000/1 shot). No symptoms either time.
Also weirdly, a few of my other old LFT tests, that were definitely negative 30mins after doing the test, have a 'positive' line several hours later. My wife's never do this - and as far as I can tell this shouldn't really happen - but it might explain some of those 'positive' tests the press found lying around the tents at the summer festivals!
Given you can spook these tests with orange juice I'm wondering if I'm just abnormally acidic!