Per the Constitution and federal law, when the presidency is suddenly vacant for whatever reason, the Vice President becomes President. But what if the Vice President slot is also vacant? The next in line for President per the Constitution and federal law is the Speaker of the House, who currently is Paul Ryan.
Michael Pence is on thicker ice than Trump, but he's not without serious problems of his own. His been caught lying repeatedly about his role in the Flynn scandal (details here) and he's also more entangled in the Russia scandal than many realize (details here).
Paul Ryan would not be a dream President for LGBT Americans, but he wouldn't be as bad as a President Pence. And arguably Ryan would be better for the LGBT community than the mercurial and unstable Trump who probably will never escape all the scandals gripping his presidency.
While he usually votes against LGBT interests, on occasion Ryan has voted for LGBT rights. For instance, he voted in Congress to ban employment discrimination based on sexual orientation.
Ryan received a 13 percent rating from the ACLU on his civil rights voting record, compared to Pence's 7 percent rating. Hence, Ryan is generally anti-LGBT but with exceptions while Pence is anti-LGBT with no exceptions.
Ryan has also expressed privately to associates that he wants to avoid so-called "culture issues" for Republicans now, suggesting he would not be on the anti-LGBT warpath, unlike Pence, who almost certainly would be.
All things considered, Ryan would be a conservative Republican President but not as bad as a President Pence. If Trump indeed does go, hopefully Pence will be gone concurrently or before him, much like happened with Spiro Agnew in 1974.