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immobilizer should not care how long your car has been sitting unused - it just cares that you have the correct Lexus key for your car, and that your ECU has not been swapped (theft related stuff)
I thought it would be right on the key cylinder but I don't see it.
Do I need to remove the radio to get to it?
the immobilizer is really a 3 part system, consisting of the ECU (ECM) and the Transponder Key Coil which is located surrounding the ignition key cylinder area and the Transponder Key Amplifier, which is located behind the radio.
this isn't an immobilizer issue at all, the immobilizer on '98-00 cars isn't a starter kill, it's an EFI kill. The car would crank forever but never fire.