As qualified as any LGBT candidate may be, this is the wrong time for such a proposal. What is desirable now is a rapid confirmation process, without giving "them" excuses to derail it, let alone rally the religious reich in an election year. (That would be a double loss. The LGBT candidate will not be confirmed and the Republican nominee will appeal to right-wing voters to make sure he is elected lest the Democrats nominate more "perverts" to the highest bench in the land.)
A well qualified, middle-of-the-road candidate that no one could rightly object to, is the ticekt. If "they" do, now they look like the obstructionists and fools.
Suffice now with the court shifting from Scalia to a centrist, and advance the opportunity to appoint justices for 4 more years.