The 31-year-old revealed details about his sexuality in a German interview earlier this week, claiming that it was a "good time" to do so.
Hitzlsperger, who is the fourth footballer to come out, went public a month after Olympic diver Tom Daley revealed that he is in a relationship with a man, said to be Oscar-winning director Dustin Lance Black.
"It's great that Thomas has come out," Lambert told the club's official website. "It's great that he's said it. Other sports have done it and football should be no different. It's happened in other sports. If you can perform on the pitch, that's all that matters."
Hitzlsperger spent four years playing for Villa.