ok, so have some resolution and thought I would document for other GX owners.
Took it to Clear Choice, independent Lexus service on 59 SW side of town.
They claim
1. They have never had to replace a compressor on a GX in the 16 years in business, so really don't think that's the problem, especially with no code being thrown.
2. There is a lexus TSB (basically help to other techs) they show me on this issue that claims that when there is a coolant leak in the engine valley this can cause the computer to turn off the compressor.
Personally, that sounds pretty strange to me as a failure mechanism. I haven't noticed coolant loss and it doesn't seem like something that would be intermittent. Seems once it sensed this issue it would just stay on.
They send me a pic showing the coolant leak mess and I do some google research that this valley leak - caused by bad Toyota/Lexus gasket - is a well known issue.
GX460 coolant leak - a hidden leak from deep in the engine (carspecmn.com)several threads on ih8mud
So it's something that is going to need to be fixed soon regardless, but I still am doubtful about the relation to the compressor.
book is 12 hours labor, they quote $1600 (says deal would be $2400), and I tell them if they are confident it will fix to go ahead.
Get the call the next day that they did the repair, took it for a test drive, got the blinking AC light but this time it threw a code (for the first time ever). Needs a new compressor. Of course!
Apologizes, says they will do a deal for $1100 for the valley leak and $900 for the compressor.
I push back and say they certainly didn't spend 12 hours on the repair and I'm worried that the timing seems like they couldn't have let the gasket cure long enough. He agrees that it doesn't take a master tech as long as the book, and there is newer Lexus/Toyota gasket that is a 3 hr cure.
They come back and offer to comp the compressor + install (but still charging for the original $1600 quote). So I got out of there for $1591 with the valley repair and compressor. Not too bad all considered, but it doesn't feel great! 2 year warranty on the whole thing.
He also let me know that besides the valley repair the transmission and radiator on the 2010-2012 are known issues. Never touch the fluid (it's a closed system I didn't plan to). And if you notice any transmission slipping it's time to sell immediately. For the GX he recommended 2015+ only.