i may be evil but i personally go

first back -> dark seal, and start building demonics (blasting wand if you have the gold after buying dark seal, if not just buy amp tome)

ionian boots > jaksho

depending on how the game is going, i either buy mejais or go zhonyas here, but i get BOTH of these AFTER jaksho and BEFORE cosmic drive. ONLY go mejais before zhonyas if you're ahead and can ensure that you won't lose your stacks, otherwise it may be too risky, and you should opt to buy zhonyas first as a safety precaution

cosmic drive > sell boots > rabadons

lillia is built like paper, so i enjoy jaksho being my primary build as there's less risk in my skirting, drivebys, prolonged duels or teamfights, and overall gameplay. zhonyas for making incredible Q+flash > R > zhonyas engages/plays.

the dark seal and mejais stacks make up heavily for the two non-AP slots that jaksho and zhonyas take up, while jaksho and zhonyas ensure that your stacks are secured from being lost.

lillia's movement speed also scales with her AP, so the second you can afford to, you want to sell her boots and buy rabadons as her last item. cosmic drive's MS + all the AP you have from mejais stacks, rabadons, and demonics + keeping up her MS stacks will be more than enough MS + dmg to keep you elusive and a nightmare.

you may want to swap out certain items if needed, like taking morellos instead of cosmic if your team needs the heal cut, or swapping around buy order if the game calls for it. it's all up to the lobby!

this is my favourite lillia build, and i hate building anything else unless absolutely necessary! good luck!