Lucky is Duster's alter ego when he gets amnesia and leaves Tazmily Village. He is first seen when you go to Club Titiboo, but is mentioned a long time before that. He is known as the man who looks like Duster, but with different hair.
Lucky plays in the band DCMC. When you first see him, he'll look exactly like Duster, but with an afro. He is the bassist of the band.
The only way to get him to join is by winning him in a game of Rock, Paper, Scissors, which is called Stone, Sheet, Clippers in this game. If you win, you can take Duster along with you, but if they win, they get Lucky. Basically, you're playing a game for his life. It's impossible to lose, but it is possible for them to beat you. Of course, if they do, something will happen and they will want to try again. If you're really having trouble, talk to the other band members. They'll give you hints, such as what they use.
Later in the game, DCMC will appear again saying that they haven't been doing very well without Lucky, and would love it if he could play in this last performance. They even brought his Brown Wig. After the show is over, and when you are fighting the Porky Clones, they'll come in and win the entire battle for you. Of course, this is after the clones have been beating on you for a while, and Vice Versa. They really don't do much damage, but it's impossible to lose after they come in to help, as these Porky Bots are weaker. This is the final time that the character Lucky is mentioned in this game.
It is said that Duster's Name affects Lucky's Name, For example, Maybe if you name him Jonny, His Band name will be Fabulous or something, But it hasn't really been tested. This probably is not true, due to in-game programming. Maybe Lucky's name will change, but not the band's name.
Lucky only appears in Mother 3 and Mother 2. This page is for the Mother 3 version of Lucky though.
A Runaway Five member is also named Lucky. But he looks nothing like Duster and is in EarthBound. He plays no important role in the story. He looks like the Pianist of DCMC.