First off, I prefer to play her in top lane, and then start roaming as early turns into mid game. lylia is a really tricky hero, and she needs quite a bit of practice to master.
she is one of the top mages to compete with Kagura and Guinevere, which is why she’s useful top. Her key to utilising the damage she can pump out is through the right items and her passive, stacked with the fact that, like Valir, her main damage is almost constant, and that makes her a formidable opponent.
I normally build a good mana-regen item, for example: clock of destiny or enchanted talisman, then build into the feather of heaven, and then divine glaive. the remaining items are up to you and your unique play style, so you know best.
Her passive, which grants her increased movement speed, allows you to kyte everyone early game, and gives you the use of not needing to buy boots if you’re doing well. it also increases damage dealt by provoked gloom ,so if you spam the gloom, then use your magic shock wave to provoke all of your glooms, dealing extra damage. this is normally enough to deal an insane amount of damage, so most enemy’s will start running, but if they don’t, remember that you are most likely faster than them, so only fast junglers can catch you.
your ultimate is used only if your desperate, but remember to watch where your shoes are, because you could be going straight into danger!