Utah is unlikely to vote in a Dem senator, but Lee is a non-starter. He’s a self-described Evan McMullin voter. Someone who values loyalty as much as Trump isn’t going to give Lee the gig when he has so many other great options.
McMullin is probably who the Utah governor would appoint to serve the remainder of the term if Mike Lee vacated the seat.
"Donald Trump's statements are beyond offensive & despicable. While I cannot vote for Hillary Clinton, I will not vote for Trump." Utah Governor Gary Herbert 10/07/2016