No, Claude Lemieux is not related to Mario Lemieux. Although he plays a very different style than Super Mario, this Lemieux was also one of the best hockey players of his time.
Claude Lemieux is one of the peskiest players in NHL history. Some people would say he is one of the dirtiest. He antagonizes the opposition like no other player can. He will do anything to get the opposition off of its game and often draws retaliatory penalties. Then he uses his offensive instincts to bury the other team by netting a big goal to help win the game.
A lot of people don't like Claude Lemieux because of the way he plays. Although he was a selfish player, he is the type of player you love to have on your team, but hate to play against. While he has done some borderline things to help his team win, and some down right nasty things, love him or hate him, you have to respect that this guy will do whatever it takes to win a hockey game. He may lack morals, but he will do the dirty work no one else will.
Bottom line - Claude Lemieux is a winner. In fact he won twice as many Stanley Cups as Mario Lemieux did. He also has a Canada Cup title and a World Junior Hockey gold medal on his resume.
Here's the full Claude Lemieux biography