Just found a good article on Cycling News about lifting in a Q & A response letter. I think this is the best explanation I have heard on why you should lift ...
Scott Saifer says:
"The question of what strength training does and doesn't do for cyclists comes up fairly often here on the forum so I gather it is a question of interest to many of our readers.
Here's the short version. Training with weights only boosts aerobic capacity in people who have very little aerobic capacity. When sedentary people start to move, they get stronger in every way. Riding a bike increases the force their muscles can generate a few times, and lifting weights increases the speed they can sustain on a bike for extended periods. Once one has been riding for a few years, as you have, that sort of cross-over benefit between aerobic and strength training disappears.
This does not mean that weight lifting is useless for cycling though as it has at least two benefits even for more highly-trained riders. One is a bit mysterious and hard to measure: an increase in toughness or pain tolerance. It is normal for relative beginner cyclists going very, very hard to feel like, "I don't know if I can do this any more" and to quit their effort, allowing themselves to be dropped when they physically could have continued with a group, or deciding to put a foot down on a hill when in fact they were physically strong enough to continue the climb.
The pain can be intense, and the desire to stop it overwhelming. Many riders will tell you that if you can convince yourself to focus on just the next few yards or the next few pedal strokes, or the distance to the next tree or something like that, it is possible to "fool yourself" into keeping going.
When you lift in the gym, if you push the upper limit of your ability (after plenty of conditioning with lighter weights so you won't hurt yourself) you can get to the "I don't know if I can do this anymore" state again and again. And guess what, if your plan is well-structured and your weights are appropriately chosen, you actually will be able to finish the sets that you didn't think were possible.
The confidence you pick up in the gym, that sense that you actually can do the things you're not initially sure you can do, transfers nicely to the bike. My clients sometimes tell me things like, "I didn't know what hard was until I did those squat sets" or "nothing in the race was hard like the lifting was hard."
Some good research has also looked at the influence of strength training on short-term, high-intensity endurance. A typical model has athletes produce a power that is well above LT, that they can sustain for perhaps three minutes. Then they do or don't strength train for several months before repeating the test at the same power.
Strength training increases the time that the athletes can sustain the same high power, at least doubling it in one study. This is not especially relevant for century riders unless they are confronting hills so steep that they are unable to ride them at a power below LT, or they are trying to keep up with other stronger riders.
If you need more toughness (the ability to keep going when it's hard or when it hurts) or if you need to sustain your maximal effort longer, strength training can help. If your legs are plain weak enough that you can't turn the pedals on steep hills, strength training can help. If you do strength train, the exercises you have discovered are okay. If you have access to a gym, I'd suggest adding hamstring curls.
Doing the strength work on your non-riding days should be fine. Pay attention to how you are recovering and if you find that your legs are getting tired and staying that way, do take a day completely off each week or more often if needed."