From the KenPom website, luck is "the deviation in winning percentage between a team’s actual record and their expected record using the correlated gaussian method."
I'm not a statistician, but I could see how losing a lot of close games would be "unlucky." In reality, some coaches and teams lack the mental toughness to win close games. Stat nerds don't buy mental toughness as a factor though. The players are just a bunch of emotionless droids who eventually throw the ball at the hoop enough times to be able to be accurately predicted.
All this is doing is comparing actual W/L to expected W/L using something similar to a pythagorean record often seen in baseball.
"Stat nerds don't buy mental toughness as a factor though"
That is literally part of what this attempts to measure, some teams are better at taking advantage of situations laid in front of them, don't be thrown off by KenPom calling it "Luck".