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stick should be on driver's side of engine.......toward the firewall and the Master Brake cylinder. It has a "T" handle on it......the oil stick is similar, just a foot closer to the front of the car.
You need to have the car warmed up, level, and idling in Park to check ATF & color..
Check your owner's manual about the procedure, and check the specs in the back on the ATF change capacity....should be in there.
That ATF is probably $8 a quart at LExus, you'll need 3 qts... how much were they going to charge for the drain / refill??