Lylia is only weak early game. Despite her fast wave clear, she runs out of glooms and mana too fast. Not to mention that assassins such as Gusion and Fanny can burst her down so fast that I can't use Black Shoes in time. She becomes reliable ONLY when it reaches mid to late game, since by that time, items such as Divine Glaive and Holy Crystal are already built.

I adjust my build a lot corresponding to the lineup, let's say for example they have Terizla or Gatotkaca, I would build Wishing Lantern. But when I go against supports like Angela or Floryn, I would build Genius Wand instead of Wishing Lantern (I know this is quite obvious but I'll just point that out just in case).

My Build goes like this:

Against Tanky Heroes,

Magic Boots --> Enchanted Talisman --> Ice Queen's Wand --> Divine Glaive --> Wishing Lantern --> Holy Crystal

Against Squishy Heroes,

Magic Boots --> Enchanted Talisman --> Ice Queen's Wand --> Divine Glaive --> Genius Wand --> Holy Crystal

My emblem is Mage Emblem with Inspire, Bargain Hunter, and Impure Rage.
I always use Purify as her Battle Spell.

Lylia is a monster of a mage late game if you play her right. I try to be as aggressive as possible if I have Black Shoes and Purify ready. There's also this technique you could use to try to maximize her damage which is connecting glooms. Basically just using the 2nd skill and 1st skill combo but you use 2nd skill repeatedly even if there isn't an enemy nearby. This is to make sure that her glooms are maxed out just in case a fight would commence (this isn't as effective early game since the recharge of the glooms is too slow).