well this build does a lot of burst damage and lowers their magic resist and armor so your nuking with the lich bane deal increased damage. you should have almost 500 ap by the end of the build plus plus the splash on your e is your best friend.

you want as much attack speed with ap as you can. the boots enchantment for extra movement when you hit single targets stacks with your q which slows the enemy and speeds you up. this allows you to use your e to take down all their health and when they start to get away you can use your heal to catch up and finish the kill.

kayle is a great farmer, you want to somewhat last hit but with your e you dont cant as much unless you just attack every minion that is low. at mid game you should be able to clear waves in a few hits.

well, max out your e first. then your a is also important for the nuking. by the time you get ap your heal will start doing more so it is viable late game