Kuva Liches steal some of your resources when you complete a mission in their territory. It has been stated that killing your Kuva Lich is the only way to recover this stolen loot.
Additionally, I find it implied, if not outright stated, that you can only have 1 Kuva Lich at a time.
Both of these points have significant impacts on the subject of killing your Kuva Lich vs converting it. Namely: if you choose to convert your Kuva Lich instead of killing it, does this count as "completing" the lich? Does it let you start another one? Does it return your resources?