Laker cheerleader? Cub player? A proper noun shouldn't change form just because it's used as an adjective. If you're referring to a player for a team called "the Cubs," then the player is a "Cubs player."
Let's venture outside the world of sports for some examples. You wouldn't call a fan of The Beatles a "Beatle fan" or a Darth Vader action figure a "Star War toy." The same logic should apply to a fan of the Dodgers. So “Dodgers fan,” if you please.
And now the bad news. Don't change a misused word if it appears as part of phrase that is itself a proper noun (e.g., "Laker Girl" or "Dodger Stadium"). Just as I could change my name to Mud Fence, sports teams are free to give cheerleaders and ball fields whatever titles they want. So enjoy a Dodgers game with a crowd of Dodgers fans, but if you're writing up your experiences for the day, don't forget to refer to the stadium by its Dodgers-given name, no matter how illogical that name may be.