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Although it could possibly be a control system fault, teh likely cause of teh symptom you describe is a low refrigerant charge level; I would suggest taking the car to a shop that performs AC charging and have the refrigerant level checked before attempting any other diagnosis. If the level is low, the compressor can shut down to prevent damage if the low side pressure drops too low, or the evaporator can freeze up , also resulting in teh compressor shutting down if the vehicle has an evap temp sensor in the system.
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I have searched a couple of repair databases and am not coming up with any consistent pattern failures on this year of Lexus that would cause the symptoms you describe. I have found many postings detailing problems with faulty solar sensors on models up to '92, but no mentions of problems after that year. I have also found several mentions of faulty expansion valves on 93 and 94 models, but a sticking expansion valve is easily detectable with pressure gauges when checking the charge level.
Something you might try: if you can gain access to the expansion valve (you might have to remove part of the case to gain access, but Im afraid i dont have an illustration of the case handy to post for you) take a look at the exapansion valve / suction line and see if it is freezing up when the problem occurrs. If you see heavy frost on the valve when the problem is occurring, then you either have a low charge level or a sticking expansion valve.