Lemony Lick-It's a A Series of Horny Events is an adult snuggle-film made by Gentlemen's Relief Productions.
Homer allowed Gentlemen's Relief Productions to film the movie in his house in order to pay back the mafia money he borrowed from, for his football gambling problem. Homer had been unwilling to do so, because he knew Marge would kill him if he did that, but went along with it after his hands were sufficiently (and literally) hammered (also getting hammered after Homer foolishly implied it was a gay porn film and that they were the "gay mafia", much to their anger).
Homer sent his family out to Santa's Village, and was anxious about how long the film production would last. He eventually bribed Lenny and Carl when they walked in during the production into being part of the movie production in order to keep them silent to Marge (with Lenny being the foulboy and Carl getting the sex scenes). Unfortunately for Homer, Marge and the kids returned home early and discovered what was going on, causing Marge to leave in a storm.
The actual plot has not been mentioned, but a brief scene that was being filmed implies that it involves female space aliens looking for planet satisfaction for a hundred years and landing on Earth.
When preparing for his scene just before Marge revealed she had returned home, Carl Carlson inquired the director on whether he should have his character have a bandage claiming he had been stabbed to cover up the fact that he had a Foghorn Leghorn tattoo to avoid any copyright infringements, although the director refused, telling him they'll take care of the matter without needing to go to that extreme.
Behind the Scenes
The title was a spoof on Lemony Snicket's A Series of Unfortunate Events".