I don't ever remember seeing Han Solo beating anybody's butt in a fist fight. He's a gunslinger all the way.
First off, Lando is the epitome of a WEAK opponent, and he made a LOUSY companion.
Secondly, any Gunslinger that can't smash a weak opponent's junk in the dirt using their melee moves... not deserving of the title.
I stand by my argument for Gunslinger. When I see him turn invisible or shoot bacta rays out of his butt to heal Chewie in a gunfight... then I might change my mind.