LaBassiere is a top three pick and will go pretty much no matter what. You just can't teach size and shot-blocking plus athleticism to move feet, and shot. He'll show very well at individuals if it comes to that because of his shot. Already getting bigger a great sign-- he'll be KAT's size or nearly there before he leaves. Few weaknesses in his game.
Murray has shown enough to be a lottery pick just in the Pan-Am Games. He's tall enough to play combo and look athletic enough to stick with European/ Brazilian pros already. TO game a worry, but that may be because of his inexperience in the Canadian "system." Even if he struggles at UK, it'll be laid at the hands of "fit", not a talent deficiency-- three PGs will soothe a lot of worries, as will individual workout. If he can shoot at a 40% 3-point clip, he's a top five selection.
At this point, it depends on play.
Briscoe, should he play fairly well, would likely be the next Cat off the table, somewhere from late lottery to mid-20's. To earn a lottery selection, he'll have to score in double figures with adequate shooting from deep (37% or so), finish well at the hoop (through contact at a 50% level), all with a nearly 2:1 A:TO ratio. If he takes over late in games as a go-to scorer, that'll earn him a couple of spots as well. Briscoe's measureables help, as he has the wing span of a Taurus.
Poythress is an interesting player. The emergence of Draymond Green and, to a lesser extent, Kawhi Leonard, will help his stock. Assuming his athleticism is hampered by injury, he's elite in that regard. He can shut down wings and has enough strength to defend PF too. That in itself will get him drafted. If he can shoot at a 50% clip inside and take enough wide open threes to show he's got that range, NBA scouts can wish enough to make him a late first-rounder. If he cans 40%+ of his threes, he'll go early 20s. If he shoots 100 of them and cans 40%, he'll go in the lottery. Needs to finish at the rim.
Lee's measureables are phenomenal. He'll need to show a capable outside shot up to 15 feet and enough dribble to get to the rim. Two dribbles without knocking it off his own knee will be key. That, his rebounding, and elite athleticism could get him drafted at the end of the first round. More likely, he'll go somewhere in the middle of the second. (If he goes at all. From all reports, Lee loves school and the UK experience.)
So, short answer long, four, maybe five Cats gone early.
