The 24-hour daylight concept seems weird to me anyway. I don't know anybody who's actually tried it.
It looks like they're in two different cages so one breeding stimulus has already been removed. At
http://www.lovebirds.co.nz/breeding/index.php it says the male is supposed to feed the female while she incubates during the day and roost with her at night. That obviously isn't happening, so maybe you'll get lucky and she won't actually lay an egg after all. But single lovebirds do lay eggs sometimes and it sounds like she might be going for it.
You might want to take that ledge out of her cage, since it looks pretty comfy and may be her chosen nest spot. She'll probably just go down to the bottom of the cage instead, but that's probably less inviting than the ledge.
It's probably a good thing if it's cool in the cage at night - that might help discourage egg laying. You don't want the birds to actually be cold of course.