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Yep, I thought that was the case too. The polymerase chain reaction which gives the PCR test its name should make it far more sensitive than a lateral flow test due to the replication process carried out by the polymerase chain reaction. In the UK lateral flow tests are used to test asymptomatic people, and not PCR tests, but I don't think that's because lateral flow tests are technically better at finding infectious but asympomatic people - it's just the government doesn't want to use the more expensive PCR tests on a routine basis.
I think that's how they're supposed to work. LFT, uh, tests are for your day to day asymptomatic testing to see if it's got into your system and you don't know it yet. It's unlikely a PCR test will detect the virus at this point but an LFT will. LFTs stop being able to detect the virus when you develop symptoms. When you develop symptoms, you get a PCR test done.