I have seen some data on that matter for the trans case because it's something I investigated recently to rebut the transphobic propaganda in Spanish right-wing media when a pro-trans law was recently approved. But you can also find similar studies for other members of the LGBTQIA+ group in Google Scholar.
There are four times more mental health issues like depression and suicidal ideation among trans people (https://doi.org/10.1016/j.jadohealth.2016.06.012) and twice more suicidal attempts (https://doi.org/10.1542/peds.2019-1183) because of what they have to go through than cis people.