Some random thoughts from someone who has spent decades both cycling and lifting (mastering neither!)...
- To those that suggest 25 reps to failure, have you ever done 25 reps in a compound exercise to failure? It's torture. Far worse than cycling intervals. The one time I thought I had a heart problem, couldn't sleep all night and actually went to the doctor was after a single 20-rep max set of squats. No thanks.
- Lifting at "only" 80-85% of max does not mean your not going to failure. Two completely different concepts. Powerlifters don't "max" (i.e. 1 rep to failure or 1RM) because it kills joints if done too often. It doesn't mean they don't go to failure at say 5 reps x 85-88% of 1RM weight.
- Be reasonable. 2 days/week 3x8 on the main compounds same weight to near failure on the last set is a good compromise.
- Actual strength is determined largely by where your muscles insert, which determines the length of you lever (leverage). Bigger muscles have slightly more leverage. Muscle type is also a huge contributor. Much of this can't be trained.
- To the original question of the OP, I think weights help a little with cycling. Mostly on jumping up rollers or the beginning of a sprint. Better to spend time cycling if getting faster is your *sole* goal