Lindsey's a former acoustic folk and banjo player. He took those techniques and still applies them to his acoustic playing, but what's really unique is applying them to electric playing. That said his acoustic voice is just as strong as his electric voice. He's one of those guys that no one can really replicate. The closest I've ever heard overall is Eric Bazilian from the Hooters. The lead singer guitar player in Haim, also cops a TON from him on the electric, but neither sounds exactly like Lindsey.
But again, it's really mainly his banjo technique applied to guitar. Add him being gifted with a unique touch, melodic sensibility, and a bare soul and you have a singular voice. Oddly he layers the shit out of it in the studio, but some of the best stuff is just him and one guitar live.