I figure the character would have to be from the late 1880s, and would need to be an asset to the League.
For example... the Phantom of the Opera for his skills in stealth and with the Punjab lasso.
John Henry
Paul Bunyan
Dr. Moreau
Dracula
Sir Percy Blakeney (The Scarlett Pimpernel)
I'd love to see Svengali pop up, since
1. He's a master hypnotist
2. He's a horrific Jewish stereotype, which I know Alan Moore would have fun deconstructing and playing with
League 1988:
Doc Brown (Back to the Future)
Lisa (Weird Science)
Macgyver
Mr T
Jack Burton (Big Trouble in Little China)
Tangina (Poltergeist)
League 1978:
Bandit (Smokey and the Bandit)
Shaft
Steve Austin (Six Million Dollar Man)
Uri Gellar
Rocky
Regan (Exorcist)
(mostly inspired by an amazing piece of alt-art i saw online featuring 80% of the above. It had Farrah Fawcett and Serpico in the 70s team)