2001 lexus rx300 starts but stops running immediatly

Check your fuel filter

l would check your fuel filter/fuel pump.

Are you using your original key? l was told there is a rolling code that gets sent to the ignition to prevent theft, that is why the keys are $300 if you loose them, l lost mine for my rx330 and had to have it specially programmed or else they said the car would just start then shut off if l just used a cut key from a locksmith.

well fisrt can you give the car gas and keep it running , and then t gets better as it warms up. if this is the case it very well may be an idle/air control valve. most common for a start and stall condition

Call the dealer they will be able to tell you better..