I used to play a purely AD Lux back when she first came out, and I ran a normal Ashe build on her. IE, Last Whisper/Brutalizer, and then whatever else you needed for the situation.
The trick to AD Lux is that she has good CC regardless of how much AP you're building on her, so you have to make use of it. She kites well, and while her shield is weak, it still makes a difference during fights.
The major downside to AD Lux is how cruddy her ult becomes for sniping the runners.
While I haven't tested it thoroughly, and definitely not recently (I wouldn't start with a Doran's Blade anymore, for starters), I'd imagine a Trinity Force or Sheen might be viable on her (skill spam is easy enough, and extra mana doesn't hurt). Mostly, I think her problem is attack speed and running out of mana, which makes her ability to chase and kite vanish without a Frozen Mallet or red buff.
A Manamune is also not a bad item on her. I didn't have too many mana issues when I was playing her AD, but I believe I did pick up a Meki Pendant sometimes (not always, but without it you have to base a lot more often), and I occasionally took blue buff.
Edit: Also, going for flat damage is usually only done when the champion has a skill that scales off of AD. Lux has none, and as such, she does more damage with 250% critical hits than she does with flat AD.
Edit 2: Also, it's worth pointing out that you don't need a Wriggle's to farm well with her during laning phase. Her base damages are still good, and her AoE + auto-attacks basically kill anything you want to kill. Early game damage output to other champs is pretty hilarious, too.