There are many different databases you can use for LGBT studies research, but you will want to use:
Academic Search Complete
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
Please check with Judy for further information.
In addition, many of the databases listed are EbscoHost databases and 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.