Access to health care is a fundamental human right, one which is disproportionately threatened for marginalized populations, particularly for LGBT persons, who often have unique health care needs. These vary from subgroup to subgroup, and here we will not attempt to give an exhaustive account of these. Instead, you can find links to relevant resources.
A publication from WHO from June 2015 thoroughly states the relationship between human rights and sexual health. Download "Sexual health, human rights and the law" here.
Centers for Disease Control and Prevention has an excellent overview over the health challenges facing LGBT people. These pages provide information and resources on some of the health issues and inequities affecting LGBT communities worldwide.
In many development countries, the right to health is being used as an entry point for working with and for LGBT people, mainly through HIV/AIDS programmes targeting men who have sex with men (MSM).
You can find recent publications on HIV/AIDS issues under "Resources".