When the A/C compressor is turned on, it adds extra load to the engine. The electronic throttle receives a signal that the load at idle has increased. The ECM adds a little throttle to the engine to compensate for the load. This increases engine speed slightly when the A/C cycles on. When the A/C cycles off, the throttle is decreased slightly to return the engine to no-load idle speed (A/C off). When the A/C is on and is running normally......and this is the same for any vehicle with A/C......the A/C compressor cycles on and off to maintain the set temperature inside the car. If you let any vehicle idle with A/C on you will hear the A/C clutch engage (clicking sound), immediately followed by an increase in idle speed, and another quieter click, immediately followed by a slight decrease in idle speed. This process repeats with the A/C on. If the engine speed don't increase when needed to run the compressor, and the engine stays at its no-load idle speed, it will slow down under the strain, run rough, near stalling (maybe even stall) and the alternator will not be turning fast enough to excite and produce a charging current. This is why the battery dies in a hurry. The cause of this problem is simple on paper, but it may be tricky to find the exact cause of the problem. (ECM, A/C amplifier, poor electrical connection, Throttle control valve or IAC valve for vehicles not equipped with "Drive-by-wire"). Have a scan performed by your Lexus dealer. It will be much faster and probably cheaper in the long run, rather than replacing alternators, batteries and chasing "Might Be's". Good Luck! P.S. When an alternator runs at a stalled/excited stage, caused by slow speed and high load, it will burn out and/or suffer damage.