ad lulu can work, but i think overall she contributes more as a support. yes fully built she is terrifying, but so is AD brand. any champ that has a stun that gets enough gold to build ie and phantom dancer will wreck people, but lulu has potential to do more than that - as a support she can wreck whole teams. Its not like it isn't doable, its just not as good as ad sona (who benefits a lot from the powerchord procs)

Tanky Lulu has insane survivability, but it relies on her being able to take a pounding before she goes down. As a glass cannon AD carry you're relying solely on kiting; Lulu is decent but not the best.

If you're going to build a non-traditional AD carry, I think you'd be better off with Kennen. Or someone mentioned LeBlanc recently, which might just work (and even if it doesn't work, it would be hilarious).

I occasionally see freeweek Lulu's try to go AS (either on-hit or actual ADC build), and it always ends up being useless. AD Sona works because she builds trinity tank, not all-out damage. Tossing in a on-hit item as your final item isn't a horrible plan for Lulu, but as many have said support mages generally only work when they're built fairly tanky. Like tanks they need to stay alive as long as possible to take advantage of their cc advantages, not win by raw damage output.