It was fairly quick for me to get to vanquishing my first one, Vordrgg Hakmo. My experience hasn't given me an impression of them as a long term fiend, at all. They need to be a continuous source of loot that improves with each subsequent encounter, among other things, so that the end goal isn't always a conversion or their weapon.
// Reward Pool
Liches, they need a reward pool based on their current rank for each encounter. Defeat them once? They drop something from that reward pool. Every subsequent encounter upgrades the reward pool, with higher ranks leaning towards the more unique items. Essentially, you are forcing your Lich out to defeat and "refine" them, and makes them prizes for co-op play. // Weapon Rerolling
You don't like what your Kuva lich is using, and you know the current Requiem mods needed to vanquish them, then you can force them to surrender their weapon, then they'll reroll their weapon for the given element they have... Based on the weapon they had previously.
// Friends we make along the way
Let their rank on conversion become their percentage chance of them joining you in your mission + their effectiveness in combat. Converting them after a certain point should reward you with a beacon that'll let you summon them in combat, for keeping them around that long.
I have issues with the thematic element of the Kuva Liches, but I'm gonna hold those thoughts until Empyrean comes into play.