A failed cat won't make it fire on only two cylinders, if it was blocked restricting flow it would only run at low revs. It should take a decent tech about an hour to establish if it has
a spark at each cylinder
compression
and fuel pressure
suck squeeze bang blow , if it has spark compression and fuel and it's all hapening at the right time it should work. if any of these are missing that's when the problems start . Electrical faults can take time to find and repair.
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Lexus UK inform me (note it has not been the dealer) that they think its a bent valve. They had already told me that the compression was fine!
I am getting very disheartened!