A few weeks back I spent a while trying to figure out a build for this, here's what I ended up with:
Ignite or Exhaust + Surge
21/9/0
Core: Rylais, Atmas, and BF Sword
You don't need a whole truckload of AP to make Lotus powerful (this isn't SR, nobody is going to stack MR against you or buy Warmogs), provided you go with your team and don't try to solo everyone like an idiot. This core will give you decent durability against the various tanky DPS, while giving you plenty of damage output yourself. Now if the game drags out really late or you get extremely farmed, you have the initial setup that allows you to add IE, LW, Triforce/Dancer, etc. Surge comes in handy here, as it gives you the attack speed needed to DPS before you can afford to actually spend gold on AS.
Is it a game-breaking, amazing build? Definitely not. But it's very fun and playable if you just want to enjoy a game as Kat.