I was fighting Lance in Crystal on my 3DS my Sudowoodo once he outsped Dragonite, Aerodactyl and Charizard and he has a Quick Claw as his held item what's the chance of that happening?

In Gen II, there was a 60/256 chance of the Quick Claw activating. (60/256) times (60/256) times (60/256) = 0.0128746033, which is about a 1.3% chance.

Hope I helped!