rbart,
How old are you and what are your fitness goals? As others have noted, lifting may not improve cycling performance but becomes important to maintain muscle mass and bone density as we age (especially past 40).
I lift year round, though like merlin mentions I struggle with fitting in leg workouts that don't hurt my cycling performance, especially 2 days later when I'm maximally sore.
I do so not because I think it'll make me a faster cyclist but because I believe it helps me stay injury free. Also, I don't want to look like T Rex in spandex (where's that Rasmussen picture...?).