Aug 4th update: two main things have been done. 1. ordered a whole assembly of the blower/re-circulation trap door/actuator and replaced the old unit, it's a bit overkill but the hinge joint of my trap flap/door is too broken to worth epoxy. 2. Had freon level checked, it was low, but not completely bottomed out. Recharged with dye. 3. vacuumed the small ambient sensor window.
All done at the mechanic. AC has been blending well and well cold since. After six days, no dye leak was found but my guy says it's too soon if it's just micro-leakage. Next oil change will check again.
Between now and next oil change, NY temperature will no longer be as hot, and I'll be anticipating anxiously, I do hope there is no leakage in some deeper components. If it's just the front condensor (within the engine bay), I'd be able to tolerate the repair but if it's deep inside the dash, my guy will freak out and I may as well trade the car in.
This whole AC experience truly worries me and triggers the OCD when it comes to buy cars. What if my next car also have AC component problem? $$$$ of repair worth it? For me, I know that the Lexus/Toyota vehicles will run for 1M miles so economically speaking, any sort of repair is "worth" it. Say, if I trade the LX for a 2021 Tacoma/Tundra/4runner/GX whatnot, I will need to put down $16000 to $24000 difference, and then that new car will one day also face AC issue. So, mathematically, spending up to $2500 repairing a complex AC issue on the LX is still worth it.