Lillia isn’t the strongest early game champion. You can use this to your advantage by invading and trying to fight her if you’re a strong early game champion like Hecarim, Lee Sin or Elise.
Post 6, fighting Lillia is going to be harder as her Ultimate R can put you to sleep. Unless you can kill her quickly, it will be difficult to win a fight against her unless you’re ahead.
Vision will make ganking harder for Lillia, especially post 6. Placing vision around her jungle entrances and in the river will make it very hard for her to find successful ganks.
Try and burst Lillia down as quickly as you can in a team fight so she is unable to use her Ultimate R to put your whole team asleep.
Keep an eye on where Lillia is when moving around the river and sieging objectives like the Baron or Dragon as she may use her E to deal some burst damage to you and your team.
Keep in mind that in team fights, her Ultimate R will be able to put enemies who have stacks on them to sleep. Avoid letting her auto-attack or deal damage to lots of champions to reduce her chances of CC’ing the whole team.
Once Lillia hits level 6, her gank and kill pressure will increase thanks to her Ultimate R. Take note that she will be harder to kill at this time.
Lillia’s early game is rather weak. If you’re a strong early game champion, try to invade and set her behind.
Once Lillia completes her jungling item, her clearing speed, damage output and gank pressure will increase. You can delay this spike by invading her and stealing away her camps.