Lane phase you are weakest. This is just a common fact. Kat scales hard into mid, late game. You want to try and farm as much you can in lane and get your items. Look for the roam. if a possible kill comes up. GO FOR IT. you are KAT you are the beast of killing. IF you don't see that happen, JUST FARM. mid game you should have sorc shoes, haunting, dorans or seekers. At this point you are very strong. You wont think so.. but you will be able to do a lot of burst and you can force bot dives with your jungler at this point. You want to use your high mid scaling to your advantage. Pick up kills, assists and farm into late. At late game you should know what to do. You want to sit in the back and wait until the mass CC from the other team is gone and than you can go in and fight and burst. You will need to q e w R. The reason is because your q e and w will be back after getting 1 assist and if you are in a sticky situation you can e out and w while e-ing to get more movement speed.

You want to Q from a distance, and w when you can DO NOT, use your e to farm. that is for escacpes or to gap close if you jungler is ganking.