I think he was lying… kind of like a honeytrap to make his father come out of his reserve. I think he only played with the thought (and with his own ass) of finding another man to try it out.
And it is left to the readers imagination whether the father was in front of the door all along listening or whether he just came to check out why he took such a long time...
Yeah, he was with his girlfriend. Since he suspects his father is interested him (and vice versa), he's lying to see how his father reacts and if this will lead to his father finally making a move on him.

sooooo, his father is dead?