How helpful is weight lifting for developing fast twitching muscle fibers?
Very good if done properly. To do so properly, however, you really should have a velocity meter, otherwise, you're just guessing.
Squats & Science | OpenBarbell V3 is a decent quality, pro-sumer velocity meter. If you're targeting fast twitch fibers, you need to consistently move weight quickly and this ensures you're in your target zone. Various muscle groups have different targets, and so deadlift, snatch, cling and jerk, squat and bench all have velocity profiles for speed-strength.
Additionally, using a velocity meter on plyometrics and jump exercises, such as the trap bar jump, is very effective.
These guys have a good outline of velocity based training: Velocity Based Training | Science for Sport
And searches for velocity based training with keywords for a sport you may be interested in should lead you to more specifics and relevant exercises.