A good-aligned human king seeks long life and the power to protect his people. They are willing to suffer the cosmetic drawbacks of lichdom, but not the risks and unethical procedures involved.
Fortunately, the neighborhood evil lich has recently been subdued. The king, who is also an accomplished wizard, uses the spell Magic Jar to possess the body of the lich.
Which benefits of lichdom does the king get to enjoy? Which benefits are lost?
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.
As pointed out to me, Liches are not a valid target due to them being Undead. However if you houseful that a Lich would be a valid target for the spell then a you should have access to most of his powers. Another problem is that a Lich's soul usually resides in his phylactery and at this point Magic Jar would let you control his body, but his soul would not be trapped. It might be possible to do the spell with the phylactery present.
You would keep everything but the mental scores and class levels. Assuming you are using the base Lich you would be able get all of their abilities. Depending on your King's mental scores you might need to modify it's skills to accommodate this.
Your game statistics are replaced by the statistics of the creature, though you retain your alignment and your Intelligence, Wisdom, and Charisma scores. You retain the benefit of your own class features. If the target has any class levels, you can’t use any of its class features.
Magic Jar states that you push your soul into the container and using the ability you can assume the form of any humanoid within 100ft. Depending on your idea justice, the king could use Magic Jar to punish criminals by taking their bodies. This would extend his life as long as Magic Jar is active, granting effective immortality.
