The light will go out immediately after adding air to the tires you don't have to drive the car. When I had this problem the dealer claimed some cars had TPMS in the spare tire. My spare tire has a rubber value stem but if yours is metal then it could have TPMS.

The best way to find out if its a bad sensor is to get an OBII cable and techstream. As long as you have a laptop its not hard to install and will tell you everything that is going on with the car. You can also clear the error code with techstream but I'm sure autozone can do that as well.

Even if you clear the error it will come back after you have driven a few miles so you may have to pony up some cash at a Lexus dealership. You may want to see how much Lexus charges to install or activate a sensor you provide. That however may not save you to much money because my Lexus dealer charges $100 an hour