How about OnHit lulu? That would make a lot more sense with her kit. She can use malady and maybe Nashers and benefit from the AP on them, plus use of Wits End, etc.
She already has substantial permanent onhit damage with her passive, so AS would seem to make more sense, just like with Kog Maw.
Plus since she deals magical damage with her spells, it makes sense to get Sorc Shoes, magic penetration runes/etc, and AP is useful. So she synergizes decently.
Unlike Kog, she doesnt have as much onhit nor the range. But her onhit is permanently up and she definitely has a better kit overall with the uberslow, polymorph/movespeed booster, shield/nuke, and grow/knockup for surviving.
Its not great, and not as good as true tanky support Lulu. But it isn't bad either and is certainly going to work better with her than true AD. AD Lulu is kind of like AD Annie. I guess you CAN but why? She has no AD/AS/crit buff at all.