Not LGBT specific, but I liked Torre de Belem and Los increíbles carruajes del Museo dos Coches when I was there. Make sure to take the tram (electricos) around.

I was only there for two days, so I can't add much more. We just went to major tourist sites and a few churches like Se.

For those that like Amazing Race on CBS, Torre de Belem was a pit stop in season two. And they had a really hot Portugese sailor as the local welcoming person at the pit stop.