I do not work for Lexus. I own a LC 500
I found that if I push the gas tank door fully open 90 degrees. Less than that, the door will probably 'fall shut' loosening the cap's position on the retaining device.
I have to push gently a little to get the fuel filler door about 10 degrees or so all the way open. It's a little different from my old SC 430.
I don't know if this works on other Lexus models.

 

Yes, I do the same thing and it works. Just have to push the fuel door open far enough so it stays put. Also I put the cap edge on the hook, not the retaining cable.