While I used to prefer Grasp of the Undying myself, Kleptomancy is ultimately better to help her reach power spikes earlier as well as stay in lane longer thanks to mana and health potion drops.
Real question, I believe, is which is the better secondary rune set?
Domination with Sudden Impact and Ravenous Hunter?
Sorcery with Manaflow Band and Transcendence?
To put the latter into context, Illaoi needs mana to do work, and since her W can proc Manaflow Band and her E counts as a champion for proccing it, it helps her stay in lane longer. As for Transcendence, a good chunk of items good for her have 10% to 20% CDR attached (Death's Dance, Black Cleaver, Trinity Force, Spirit Visage, Spear of Shojin, Iceborn Gauntlet, etc.) and making use of the excess CDR seems really good.
[Note: I tend to build Iceborn Gauntlet as the armor item as the AoE physical damage and AoE slow synergize so well with W and Death's Dance; in fact I tend to build it more than Black Cleaver as the Phage proc is mostly wasted on her and the armor shred, while easy to stack, is honestly kind of wasted unless a majority of your team is AD or the enemy is building armor; thankfully Kindlegem builds into Spear of Shojin and Spirit Visage as well]