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 turns out the cat that Alf grabbed isn't 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 warned not to try to eat Lucky. In the first episode (A.L.F.), 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 was a bagel, but Willie caught him in the act. In Something's Wrong With Me, ALF said that one of the only ways to cure Melmacian hiccups is to drink cat juice. When the Tanners give ALF some (placebo) cat juice, ALF thinks the Tanners sacrificed Lucky, only to be told it was a stray. In the same episode, Kate has said to Alf, "Anything you do to this cat, I'll do to you" .
ALF seems to have befriended Lucky to some degree, at one time showing the cat slides from a family vacation, and another time saying that he will not make a meal out of Lucky, as he values the trust the Tanners have in him not to do anything untoward with their cat.
Lucky's breed is American short-hair.
ALF's nickname for Lucky is "Luck-meister".