When Lane winks at the audience, he's no longer playing a character -- he's playing himself. For years Lane has been doing this schtick in which he becomes sexually aroused (and nearly has an orgasm) when he suddenly bumps into a very good looking (and sometimes scantily clad) young guy. He did this schtick in Love! Valour! Compassion!, an episode of Sex and the City, a talk show with Matthew Broderick, an on-line skit with Cheyenne Jackson, and probably many other occasions. It's hilarious and it works in Gary. David Hyde-Pierce would also be able to pull off the role because he's known for the same type of schtick, and the audience knows he's openly gay.
Given the time frame, the location, and the situation as depicted in Gary, I don't think an ordinary clown (who has recently avoided a death sentence) would openly display the sort of arousal handling male corpses as Lane does. If he did, he would be setting himself up for immediate execution. I doubt if that situation would get many laughs and neither did Gary early in its run before Lane and the others began incorporating their schtick into the play. Just saying.