I haven't tried much in terms of lube and diapers, but I never find my diapers breaking down or anything with the Equate Liquid Personal Lubricant (water based) that I use padding up after big time. Not a whole ton of it leaks out into my padding though so I don't know how much you plan on using that might affect the performance of your diaper.
J-lube powder is fun. You can either mix it into a water based thing (a little bit goes a loooonng way), or sprinkle some into a diaper like baby powder and feel it get slippery as you wet.
I've also had good luck with Johnson and Johnson baby lotion. Not really a lube per say, but it stays nice and slippery if you rub some in before padding up, and I've never seen it attack the elastics. Just be sure to get it all off your hands before grabbing the tapes or touching the front of the padding.