The lottery's rights are exclusively held by ESPN or in the past, NBC; NBA TV can't carry them because it's mainly an ESPN production, and on NBA TV it would have a small audience because not everyone carries it.
That said, last night's coverage was terrible. Why did they have to make it look like a 'dark room and lasers and fake tension' game show-like setting? It's 14 teams getting random balls picked out of a chute. And it used to be done in ten minutes on NBC during halftime; why stretch it out to a half-hour so you can have the Countdown cast put in their piece (on another note, Jalen 'read...words...off...teleprompter...stiffly' Rose remains the worst sports commentator in television history).