Sounds like the problem is in the whole climate control system that controls the heat and the A/C.
The A/C clutch relay is controlled by the A/C Amplifier (computer) based on several inputs.
The A/C pressure sensor won’t stop the heater from operating.
How did you check for system faults?
Im having the same exact issue with a saturn, it seems to be fairly common, were you able to find out what was causing the problem, with it needing to be jumped at the relay, that tells me the problem is occuring before the relay, everything in the system works after the relay point when jumoed at the fusebox. Ive tried a pressure switch for shits and goggles, that didnt solve anything.
A Saturn and the OP’s Lexus are two entirely different vehicles…
You will get much better responses by starting a New Tread with all your vehicles info (year, make, model engine etc etc, and what it is doing or not doing in as much detail as possible… We will help you as much as we can, but AC work is best left up to the Pros…
Details are the key, if you do not provide much detail, your answers will reflect it…