Once during a feeding frenzy, ALF is believed to have eaten Lucky, but he is later found. ALF ran off looking in the outside world, but is caught by a rescue shelter worker who doesn't know what kind of creature ALF is. ALF tricked the rescue shelter worker into releasing him so that he can grab the cat that looks like Lucky to bring home. Although it is explained that ALF did not actually grab the real Lucky, he still was not allowed to eat the cat he just took from the shelter. ALF actually tried to hypnotize the cat the same way he did to Lucky at the beginning of the episode.
(Episode: Looking for Lucky)
Throughout the series, ALF was never allowed to eat Lucky. In the pilot episode, he asked "Do you have a cat?" when he was requested if he would like anything to eat. In Looking for Lucky, he tried to hypnotize Lucky into thinking he's a bagel. It is possible Lucky did fall asleep by the hypnotism ALF did on him. In Something's Wrong With Me, ALF said that one of the only ways to cure Melmacian burps is to drink cat juice (the hiccups are actually still cured if ALF thinks something he drank was cat juice).