I found no credible source that claims Quinlan Vos was officially based on “The Dude” from The Big Lebowski.

However there is evidence of informal influence / homage:

• In The Clone Wars episode “Hunt for Ziro”, Vos uses a line very similar to “Well, that’s just your opinion, man,” a signature line of The Dude. (Wookieepedia)
• Some commentators and fans observe a “laid-back, rule-bending” vibe in Vos’s depiction in that episode and liken it to The Dude’s demeanor. (outoflives.net)

If you like, I can dig into interviews with The Clone Wars writers / Lucasfilm to see if any have confirmed this influence. Do you want me to check that?