Lillia's Skill Max Order: Q → E → W
Level 1: Conduct the Quinn Cheese level 1 from the bush and run her down if she tries to fight. You hard win the trade no matter which ability she starts, so play as aggressively as you can. Lillia's Q range is 485 units at the outer edge, which is 40 units less than your AA range. Stay in AA range, and if you do this, Lillia can't land her Qs on you. If she gets close to you, stay in the outer edge of her Q when she launches it so it doesn't deal as much damage.
Level 2: Lillia has her W/E now. She'll go E if she's behind to get last hits, and W if she's more aggro, but regardles you aren't worried. Zone her off EXP with your body and if she steps near you, punish her with hard trades.
Level 3: Lillia's W can be cancelled with Quinn E, so if she lunges at you, be sure to vault her mid air to cancel her ability. This is important because if she lands she deals 200% increased damage, but if you vault her in mid air you prevent this damage from hitting you. I would typically recommend to save E to cancel her W in this matchup if you're able to react quick enough to cancel her W in mid air. It's a really good disengage tool because Lilia relies on stacking her passive with abilities to grant her Movespeed. If she doesn't land abilities on you, she won't get movement speed. Her passive makes her lose stacks after 5 seconds of not landing an ability on you.
Level 6: This is where the matchup gets scary. Don't be low in lane because if you are, she can easily put you to sleep and kill you. Ward deep post 6 because she sets up incredible ganks. Cleanse/Merc Treads are good to prevent her R from being as lethal as it could be.
This matchup is easy early game.
Your E pushes you outside of her Q range, and your E cancels her W dash.
Use E aggressively in this matchup because it pushes you outside of her Q range. If she Qs during your E, she can hit you at the sweet spot if she times it right, but if you E during her Q, you can dodge her sweet spot. The best bet is to E first so that she can't get the chance to hit you with the edge of her Q.
Pre 6 play super aggro because you hard win.
Post 6, if you get tagged by any ability then she can put you to sleep. Run cleanse if youre afraid of post 6, otherwise just try not to be low when she has R.
She cant 100-0 you, but her R is perfect for gank set up.
Ideally, do not push up in this matchup post 6 if you dont know where enemy JG is. If enemy JG is far away, you can push up because her sleep isn't enough to 1 shot you with null-orb.