Just a general FYI on tests, as I was at a 2 day trackday last week and we all had the same thoughts. Note that I have a couple of degrees in Biochem and genetics from UMIST and Sussex, and wrote my understanding of the differences, a friend who is a Principal Lecturer in Biological Science wrote this excellent explanation of why LFT and PCR results can differ. Which one is "wrong" is open to debate as they look for different things.
A Lateral flow is good (generally) for say you're 'infectious' - ie. you've got live virus in your airways that has the potential to infect other people. You need to become infected and the virus replicate in your system and then be released again into the airways. Generally you will go positive 2 - 5 days post infection.
The LFT looks for viral proteins in your airways, indicative of live virus.
PCR tests for the viral genome and is much more sensitive as in theory it can detect at single molecule level. (In reality probably tens).
This means it can pick up early infection - partly as the viral replication cycle also produces bits of RNA in your cells which means that there's more RNA than there is actually viral particles. It is possible to fight off an infection without it entering your system, a lot of people never seem to suffer from colds, but they still catch them, they just figth it off before the infection establishes..
This also means that people can stay positive to PCR long after they have actually cleared the live virus because the PCR will pick up bits of viral RNA hanging around that are not infectious complete viral particles, but effectively bits of 'dead' virus and viral replication intermediates.
This is also why it's possible to be PCR positive and have no culturable virus - there's a nice paper by La Scola et al that is the best study on this.
Essentially if you have a high PCR Cycle threshold (which means a low amount of detected virus) its unlikely you have enough complete virus around to be able to infect it deliberately in cell culture, let alone infect anyone else.
So lateral flow isn't entirely a matter of being 'less sensitive' - it's measuring a different thing, as it detects the proteins on the outside of infectious viral particles... so if you are LFT positive, you really should keep yourself to yourself.
I'll go back under my rock again now, back to talk of cars
Paul