Can't comment on the Lilly padz since I've never used them, but it looks like I don't have to!
I have used a band/girdle after my last few kids (I'm expecting #8) and I swear it makes a world of difference. After one of them I bought one of the bands that is specifically made for postpartum, but hated it because the giant strip of velcro was just uncomfortable. I ended up returning that and going back to just regular shapewear (I prefer the ones that are like bike shorts with a super high waist). A lot of people figure I do it because I don't like the bloaty saggy belly look, which is partly true, but I have found that it really makes a difference in the way my insides all settle back into where they should be. After a couple of my babies things had problems resettling and it caused a great deal of pain. We checked for appendicitis, gall stones, the typical "I feel like I'm going to die b/c my insides are hurting so much" kind of things, but all of that has always been clear. The other option that was presented to me was that sometimes as your internal organs return to where they should be after your uterus shrinks, they may not settle in right as they should be at first and that it can be extremely painful. Whatever it was that caused the pain after those babies, it was much worse than my labors (pit induced, w/out pain meds). Sure enough, when wearing something that held everything in for the next couple of babies, I was able to avoid whatever had been so painful with the others. It's possible it was just coincidence, but I'll take whatever I can get! :)
Oh, and the added bonus is that my waist/belly/hips size shrinks much faster, returning me to normal clothes very quickly!