Greg Sargent of The Washington Post wrote an excellent and well researched column yesterday (link here) with the title "Yes, Donald Trump ‘lies.’ A lot. And news organizations should say so."
While the piece focuses more on the quandary the journalism business finds itself in while covering the habitually dissembling Trump, it also underscores how the President-elect is a shameless and profligate liar.
This is why many people, myself included, do not believe Trump's claims about being pro-LGBT. You simply can't believe a liar. Trump lied so many times on the campaign trail, as was well documented by fact-checkers, and has continued incessant lying since the election.
Until Trump does something that is actually pro-LGBT and not just lip service, we must assume he'll cut the LGBT community off at its knees. You have to conclude Trump is lying until he proves that he's not, something that he's rarely able to do.