Similar to a black sheep when talking about familial relationships, a lavender sheep is that member or members of a family who are outcast, ignored, or otherwise ostracized by his or her own blood relations owing to their non-heterosexual identity.
This is an especially difficult label to bear for younger people. Many are the gay youth that are thrown out of the house once it's discovered they're gay, or bi, or transgendered. Unlike many racial, cultural, social, or religious minorities, a gay youth cannot usually go home after a day of being teased by peers about his or her minority status and expect to find a family full of people just like him- or herself willing to provide comfort and empathy.