I would put the lights on to encourage the growth of anything photosynthetic that might be attached to your live rock.
Like hair algae, diatoms and slime algae?
I agree with Imsobored. You aren't going to kill anything by leaving the lights off during the cycle, and at the same time the only thing you're going to "grow" is nuisance algae. Your tank is a cesspool during the curing process, and you're likely to get all the nasties we so despise in this hobby if you give them light during this time. I think the main reason people want the lights on during the cycle is for the coralline algae.. don't worry, if you even have a tiny bit of coralline on your rocks, it will be fine in the dark for a month or so. Having your rocks covered with nuisance algae actually inhibits coralline from spreading more than anything else. My pico is living proof of that right now, the spots where my snails have cleaned off are sprouting the bright purple stuff while the rest is a drab brown from the algae :maddown:
I would, however, run the light in your fuge in a reverse-daylight schedule (on at night, off during the day). This will help keep combat the common pH swing that occurs when the photosynthetic beings in the display don't get light and aren't producing oxygen.
You may also have to start the cycle with a shrimp or something similar. Sometimes live rock die off isn't enough.
EDIT:
I keep the lights on an hour or two a day.
This is fine. I wouldn't have them on a whole lot more than that.