I'd take Barnes over the 12 pick every day of the week and twice on Sunday. He fits this team perfectly. He can start at SF, can play PF, is a good defender, good team player, can shoot, stretch the floor, etc. He just fits perfectly. Right age, right talents, comes from a winning organization. Barnes is better than the 12 pick any day of the week. I'd trade that straight up.
The Burke for Lee part? Neither team cares about either player. Lee is at least an NBA player. Im not sure you can say that for Burke.
The reality is that trade would probably have to be:
Burke, Booker and #12 for Lee and Barnes.
Trading Booker is tough, but reality is, Booker probably isn't in Utah's long term plans, while Barnes could be. I'd still do that trade.