Damndest thing about free throws, too. There are some things that can be fixed with practice, and some things that can't. Bad form, inconsistent release point, etc. - you can work with them, make them shoot 1000 the right way, and work that stuff out. The mental part, though, just doesn't always translate between practice and games.
You know who shoots the most free throws on Earth? DeAndre Jordan, Andre Drummond, Dwight Howard, guys like that. The worst free throw shooters in the NBA. These guys aren't lazy or indifferent - you don't get as good as they are without being willing to work. They are surrounded by the best coaches & psychologists money can buy. Their coaches insist that in practice, they are just fine - guys like that often hit 75% or better in an empty arena. Get in the game, and it all goes wrong.
I've heard DeAndre Jordan say that when he steps up to the line, the first thing that flashes into his head is "don't wind up on Shaqtin' a Fool. Just make sure you hit SOMETHING." Once those thoughts get in your head, it is hard to get them out, and they mess with you.
I think the pressure of the game definitely got into Kyle's head the other night. He is an emotional guy, and it got the better of him. I'm sure he is going to spend extra time in the gym, but you never know if it is going to help until you get back in that situation again. Hopefully you can overcome it, but so much of it is baked into your mind over the first 20+ years of life, you can't always overcome it.
Danny Fortson fixed his free throw shooting pretty much overnight. He had a bad FT shooting game in a win against Arkansas, which had been attended by the President at the time, Bill Clinton. Clinton actually spoke to him after the game, complimenting him & mentioning that if he was more consistent at the line, he would be unstoppable.
Fortson was so struck by the interaction that he just hyper-focused on it, and was instantly, and for the rest of his career, good at the line (75-80% for years in college & the NBA). His brain responded to that stimulus. Some people, maybe that messes them up worse. You just can't tell.