The question on whether to lift for cycling or not has been argued for years.
Mention gym work on cycling forums and many will either turn off or look for the flame key. The controversy is about whether lifting weights in the gym will transfer directly to strength and/or endurance on the bike. Just for a moment, let's forget about whether increasing your strength in the gym will help your ability to pedal the bike as a direct result of lifting heavy weight.
I suggest that the gym is a place to do other things to improve your body and is a critical part of anyone's training program. This of course assumes that the objective is to become a better athlete and/or a healthier person (not always the same thing).
Spending huge amounts of time sitting on a little seat while in flexion and moving only your lower extremities is a recipe for muscle imbalance. This is particularly troublesome when you don't stretch tight muscles or possess the ability to properly activate the abdominal wall (especially the transverse abdominis). These imbalances easily translate to posture issues as well as joint instability on and off the bike, and they affect your life and health in general.
Gym work that includes corrective stretching, stability (static and dynamic), strength and power work (in both open and closed chain moves for cycling), is the chance for cyclists to tune up the supporting muscular and related systems of the body to better support such a limited movement and non-weight bearing activity such as cycling. Gym time is the chance to balance out what cycling does to our bodies during the long season. I advocate gym work year round, but I'll leave that one between me and my clients.
Cycling is a sport pretty much completely occurring in the sagittal (forward) plane. On the other hand, most injuries in happen in the transverse (twist) and frontal (side to side) plane. Working your body only in the sagittal plane means that muscle imbalances can (and often do) occur to stabilizers around the joint; the weakest parts. If you're a pro and your job is only to bike, then you might be able to justify avoiding training in other planes.
The problem is that most of us aren't professionals being paid to pedal. We still have to live, work and play in the real multi-plane world. So on the weekend when you decide to play tennis or soccer with your friends or help your mom move a couch, you might quickly locate some muscle/joint imbalances the hard way via injury.
Move to survive
Paul Chek developed a way of breaking down movement into what he calls the Primal Patterns. When we were hunters and gatherers we had to push, pull, lunge, bend, squat and twist or you didn't survive very long. I think it is sad when someone considers them self an athlete, yet they cannot perform these basic fundamental movements even without weight.
While we're no longer hunters and gatherers in the true sense, our bodies are designed to move in these ways. In order to be a healthy functional person, why wouldn't you want to be capable of these basic movements? I promise that you still push, pull, lunge, squat, bend and twist in other sports or daily activities.
Want another reason to hit the gym? The brain will only allow you to lift as much weight as you can stabilize. If you try to generate more force than a joint can stabilize, the nervous system will actually inhibit the muscles around the joint. Many strength gains are attributed to neural adaptations not hypertrophy.
This is a good thing for cyclists because then you can get stronger without increasing weight or size. Stabilizing the joints enables you to work the muscles for greater gains. Of course, this takes the correct application of sets, reps, tempo, rest, and load as well as exercise selection.
Machines are garbage!
Here is the ultimate catch: The gym has been poisoned and polluted ... it is a place full of garbage machines that create dysfunctional bodies and would really do more good serving as boat anchors (Hammer Strength, Cybex or whatever). You live, work and play in a closed chain environment (when your distal extremity cannot overcome the resistance force, such as when you do a push up your body moves away from the ground vs. the open chain bench press). Machines are pretty much all open chain environments that do nothing to teach you how to integrate your muscles and joints together; they do nothing to teach you how to move your body while stabilizing it.
Instead these large metal contraptions designed by engineers who clearly know little about how the body works train you like a bodybuilder by isolating muscles and effectively building dumb ones. As a cyclist you want a harmonious synchronization of muscles powering the stroke. You don't want a bunch of individuals working solo. Machines also can set you up for injury in several ways.
Learn to correctly use free weights by performing movements with correct posture and form and you will have functional carryover to the real world and sports.
No more sensory motor amnesia in the abdominal wall
Finally, gym time is a great chance to learn how to activate your deep abdominal wall. I run into very few clients that can do this before we work together. This is important for so many things from digestion to breathing to avoiding pronation injury. For cyclists, learning how to activate the TVA and stabilize the pelvis against the forces of the psoas and quads as well as stabilizing for ALL gym movements is critical to your success.
Learning how to take a diaphragmatic breath for example, has ramifications for your oxygen intake. If your shoulders and head are forward and you have a rounded upper back (thoracic kyphosis) you're effectively stuck in expiration and are possibly (probably) reducing the range of motion for your diaphragm by a third!
If you want to read a great article about gym training today as it relates to functional activities, read Paul Chek's Should Athletes Train like Bodybuilders. On his site you'll find other fantastic articles that might open your eyes. Many are indexed under on the "Articles" page on his site. I highly recommend the nutrition articles, but that's another mortar round.