OH! I just saw that you wanted it LGBT-focused. Ok, how about this, this might get them to talk about their identity and visually show that everyone has different segments to their identity. Have them go up to the front of the class and have spectrums up there like this:
Masculine |------------------------------------|Feminine
Butch|--------------------------------|Femme
Male |------------------------------------| Female
Gay |--------------------------------------|Straight
Top -----------------------------------| Bottom (um, 18-23, maybe not, lol)
Dominant |----------------------------------|Submissive )personality type)
And some others...each person goes up front and marks where on the spectrum they are for each of the items. The idea is that everyone gets a better idea that there isn't just ONE identity for people, there are many. This might be a little intimidating for that age group. I've done it in groups of like 18-40 and the older people were usually more comfortable with it. Good luck!