There are many different databases you can use for LGBT studies research, and many are through the EbscoHost platform.
You will definitely want to use:
Academic Search Ultimate
LGBT Life with Fulltext
Women's Studies International
And, then, depending on your focus, there are other databases to add such as:
America. History and Life
MLA International Bibliography
Psychology and Behavioral Sciences Collection
There are other databases through the ProQuest platform:
In addition, those EbscoHost databases can be searched together to remove duplicate results. Once in one database, click on - choose databases, and either add all, or choose additional individual databases.
The Proquest databases can also be searched together, click on - change databases.