From the case summary it was a neighbor (another dude) who had apparently hooked up with one of the guys before. He didn't take the breakup very well and had been harassing the guy he hooked up with. The neighbor called the cops and reported a crazy man with a gun in the other apartment. That gave the cops probable cause to enter the apartment where they found the two guys going at it in violation of the sodomy law at the time.

ETA: The case was Lawrence v. Texas