I do not believe there is a specific order. The position of the tires change as rotation of the tires occurs, but the position on the gage stays the same for that tire. The spare is easy to see because the pressure does not vary much as the tires warm when driving.
I always keep the spare over inflated so you never have to guess. But the other 4 are all listed together. If the alarm goes off for low pressure, you should be able to look at your 4 tires and see the low one. This is what the system is designed to do.
Some technical info: there are 5 "slots" in the computer's memory for TPMS sensor IDs. When the dealer programs these in, they put them in some order and if they tell you what the order is, you'll know. But keep in mind that if you physically swap/rotate tires, the system has no way of knowing where each one went... so you'll have to deduce the new locations based on how the tires were rotated.
Also, if you want to check how they are currently ordered, just let some air out of one, note which one starts showing a lower pressure on the display, then pump it up again and repeat with the other 3 tires. Note that the pressures don't necessarily update in real-time on the display. It may take a couple of minutes.
Check out Carista OBD2 app for Android: you can change your Lexus Personalized Settings and diagnose all Lexus/Toyota ECUs.