With Lillia, I tend to go for a full clear starting with leash. You can take almost every camp without taking much damage as long as you are kiting. Her move speed allows for fast travel between camps, and you can throw your E into lanes for poke while you are clearing.

Lillia is pretty bad at 1v1, but with phase rush you have very good escape to kite back to your laners. You should be safe to contest scuttle because you are very fast while farming.

You want to get your passive up off the nearest camp, then start the gank with a far away E. Pre 6 you want to land the E on the champ to slow them because that is your only cc. Post 6 you can aim the E at farm to keep your passive up if you are worried about landing it, then use ult to secure the kill. The key part of ganking is to keep your passive up the whole time, if it goes down you are vulnerable to counter ganks.

Lillia is noticeably squishy right now, with no passive sustain or resistance. Because of this, you want to kite in and out of teamfights, applying your passive to everyone. When looking to ult, lob your E into the backline, then Q + W the frontline to hit everyone with your passive. W is best to break the sleep with, but Q does high damage aswell. Pretty much just spam your abilities while running in and out like a singed.