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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.
That's not my understanding.
PCR is more sensitive than LFT. If you are infected on day 0 a PCR might detected it on day 3-30 and an LFT on day 5-9.