Looking back through my databases, the best season I ever had in terms of cycling's markers, climbing and endurance, I lifted quite a bit, usually twice a week. I only lift to improve cycling performance and general resistance to injury.
Starting in October, I did a progression. I started by working up to 3 sets of 30 of 8 exercises circuit style, resting only enough to drop my HR below 100. I used the same weight every set, enough for failure at about the 30th rep of the last set once a week. Then I went to hypertrophy, 3 sets of 12. Then strength, 6 X 5. By the time I had done strength for 6 weeks, it was the end of February. I switched back to 1 set of 30, twice a week for 6 weeks. For the rest of the summer I did one set of 30, once a week, not working to failure.
The objective was not only to get stronger, as in lift more weight, but not to get injured, and to still be able to bike. I did all my lifting after biking on my rollers or outdoors, or spin class. That way it didn't cut into time on the bike. I often reduced intensity on days following weight workouts. I lifted on Tuesday and Thursday and did a competitive ride on Sunday, every week. I usually hiked on Monday and biked Tuesday, Wednesday, and Thursday, then either did a short roller session on Friday or used a Stepmill at the gym.
I'm following this program again this year, with good results, though I've added more rest days since I don't recover as quickly as I used to.
Exericises:
Leg sled
Seated cable row
Back machine
Squats
Pushups
Straight legged deadlifts
One-legged calf raises
Roman chair
Lat pull-down
I don't follow the progression on the back machine, SLDLs, pushups, or calf raises, instead keeping these at 3 sets of 30, then reduced to 1 set. I stop squats and lat pull-downs around New Years. With luck I should be able to keep this up until I'm 80. Now that I'm retired, I'm also downhill skiing on Thursday, so that day I ski, do a spin class, and lift.
I eat so as to have a weight peak around New Years, then slowly losing weight going into the season, from 5-10 lbs. depending on how heavy I got. Can't climb if I'm heavy. My summer weight hasn't varied much in 20 years.