This is my first guide but I was playing around with this and decided to share it.
This is for Attack speed / on hit magic damage Lulu. With this build you can easily melt your enemies and keep them afraid to farm. It will be a slow early game until you have your Berserker's Greaves and your Malady, but after that you will have enough attack speed / dps to constantly harass and keep the enemies at bay.

Pros:

• Great lategame
• Melts enemies
  

Cons:

• Item dependent
• Slow early game
• Squishy until you learn her abilities.

These are the runes I chose,

• x9 - 3 of your main items are going to do on hit magic damage.
• Greater Seal of Defense x9 - Armor...
• x9 - Magic Resist...
• x3 - The start of the bread and butter.

For masteries, I went with 29/0/1 the one point in utility is for the flash CD. These masteries pick up the attack speed, armor pen, CDR, and magic pen that will help you maximize your damage output.

Core Items:

• Berserker's Greaves
• Malady
• Madred's Bloodrazor
• Wit's End

Once you have Berserker's Greaves and Malady, you will be sent straight to H.R. for all the harassing you will be doing. Madred's Bloodrazor is the icing on the cake more AS and 4% of their max health this is where you can take out that tank with 4k health and secure that Ace. Wit's End, same thing more AS more Magic Damage.

Sugested Items:

• Phantom Dancer - AS, little bit of move speed, and crit.
• Frozen Mallet - Helps with chase and 700 HP
• Ionic Spark - chain lightning, but PD has more AS and move speed

Obviously, replace some items if you need more MR or armor

Pix, Faerie Companion - They will nerf this enjoy it while you can once you get close to 2.0 attack speed it is a constant machine gun firing.

Glitterlance - 80% slow?!?!? 1 point max it last

Whimsy - Great ability, 2 enemies chasing you, cast on yourself for movement speed, 1 enemy chasing you cast on them to disable/slow Max this second

Help, Pix! - This is how you survive, you wont get much scaling because your not stacking AP but it will give you enough to get away if you need to. YOU WILL NOT BE CASTING THIS ON AN ALLY UNLESS IT IS TO SAVE THEM IF YOU SPAM THIS IT WILL KILL YOUR DPS, however, casting this on an enemy gives you sight and Pix will shoot from the enemy's location. Max this First

Wild Growth - This is a really cool spell the AOE slow around the person its cast on plus the bonus health. Team fights save it for when enemy team commits to fight and cast it on the tank if needed, if not save it for an ally who is getting low.Put a point whenever it's available

Must Have
Flash - Always must have.

My preference for second spell
Heal - Helps in early game sustain. I know, "Heal sucks, blah blah" pick a different spell this is my preference

Other Options
Ignite - Finish them off
Ghost - Chase / Flee
Surge - Maybe? Wont really need it late game might help in early/mid though
Clairvoyance - Ehhh.... It gives the wrong idea but it is useful to your team. Make sure to tell them you are not support if you pick this.
Teleport - Always a useful spell

No, just no.
Exhaust - Glitterlance, Whimsy, and Wild Growth 3 slows dont think you need 4
Revive - Do I need a reason?
Smite - Get your *** out of the jungle!
Cleanse - I'd rather replace an item and save the summoner spell
Clarity - Were you paying attention? This is Attack Speed you wont use that much mana.
Promote - Only exception is if you are with a strong pusher in bot lane even then kinda meh

This champ is fun to play I didn't care for her support (more boring than most support champs) but this AS build is fun effective and worth a shot. If you got the runes try it. Once you get that support mentality out of your head and start thinking like a ranged AD with a butt-load of utility you will love this build.

Thank You
Tyrsyn