A lich is not a valid target for Magic Jar
You can attempt to possess any humanoid within 100 feet of you [..]
The description of Magic Jar specifies the target for possession is a humanoid. Liches are not humanoid, they are undead. Therefore, RAW this scenario doesn't work.
Assuming you'll want to houserule to allow it though, the next problem is that as per the description in the MM a liches power has little to do with its body and all to do with the Liches souls connection to its phylactery, so even then it's doubtful that possessing the body of a Lich would confer any advantages over possessing the corpse of a spellcaster (which of course doesn't work with Magic Jar either, because corpses are objects, not humanoids).
Assuming you'll handwave that by saying the phylactery somehow maintains the body of the Lich even with its soul no longer inhabiting it, the next problem is that as per the description in the MM a Lich begins falling apart if its phylactery is not regularly fed with living souls. While it's never specified exactly how regularly this has to happen, presumably it's intended to mean often enough for the ethics of this plan to not work out as well as you might hope.