I don't know about succeeding on the parent schedule...it feels more like existing some days, particularly this one.

I go to bed late. I wake up early. Most days like today I wake up and when the kids leave for school I go back to bed. That's when I most often become lucid but I doubt it's just the schedule alone. My dreams have been my domain since I was young without any guiding factor. I think I just pay better attention these days.

I know I'm good with awareness and that helps.
I know I'm often very tired with an erratic sleep schedule and that helps.
I have good recall and that helps.

The thing is...I didn't become this way with the effort to lucid dream. My mind has always just been the way it is. My sleep schedule likely only helps the effort and even that is a product of enjoying my adult-time after the kids go to bed but being responsible enough to sacrifice my own rest for their needs. It's not a purposeful effort to achieve better dreams. It's just how my life is right now.

Still, on the days I do get plenty of rest (as in the summer during school vacation) I think varying the sleep schedule does help produce quality lucids. On the days when sleep is a luxury easy to indulge in I find it's good to sacrifice a day or two. The payoff is a better chance at a lucid dream and a greater likelihood of a lengthy LD.