Lambda began as a GLBT activist organization in 1971 at then West Georgia College. The organization was created by students and faculty member Dr. Ara Dostourian and coordinated with a similar group based in Atlanta. They were inspired by the 1969 Stonewall Riots in New York and the related organization of pride marches across the country. Dr. Dostourian, a University of West Georgia Professor Emeritus, helped to grow the organization and push for the rights of GLBT persons both on and off campus.

The group has changed its name, form, advisors, level of outreach and support, and membership since its creation, but throughout its existence has advocated for the equal rights and positive visibility of GLBT persons and the LGBTQ community. From the mid-1990's to the present, the organization has undergone various changes in purpose, structure, and name from the Gay and Lesbian Alliance to the Gay Bisexual Straight Alliance to Lambda.

Lambda's mission was to "foster and create an open, honest and supportive environment for gay, lesbian, bisexual, transgendered and questioning persons and their allies in and around the State University of West Georgia." The group pushed to "promote education of LGBT history, rights, struggles, and issues; to celebrate the diversity that exists among the UWG community; and to inspire understanding and acceptance, especially of LGBTQ persons." In order to enact these goals, the group met weekly and hosted a variety of events on campus.

Lambda was officially re-branded as the Queer Student Alliance (QSA) in the spring of 2019. The Queer Student Alliance helped plan and host Carrollton's first LGBTQ Pride event in October 2019.