Litherites are the Paladins of the In Nomine universe. Not only can’t they lie (common to any Seraph), but they cannot allow deceptions of any sort to stand. They present problems for both party and setting while simultaneously getting to play the part of sanctimonious goody two shoes.
Parties must work around a Litherite in their midst so that it wont reveal their activities. They also need to actively constrain the Litherite against betraying the truth about heaven and hell. And in exchange for making everyone else’s life harder, the Litherite gets play a character who doesn’t care about blending in (which often includes blatant disregard for consequences).
Litherites have no role in the Symphony. They are barred from taking one. That means no ID, no job, not even someone who can vouch for or interact with the character on a daily basis. If they were all 1-job demon killers, this might make sense – but as a whole they’re supposed to be patrons of researchers, journalists, and archaeologists (three groups that are especially unlikely to listen or report back to someone with no bona fides).
It is true that this lack of role makes it easier to detect when a Litherite is up to something, but they don’t care. Either there are no drawbacks to being a Litherite, or they are so flawed in practice and design that they should never be able to succeed at their main objectives. Neither approach makes for a particularly playable character.
My personal suggestion is that Litherites should be reserved for antagonists or for parties where all the players are eager to deal with having a Litherite in their midst. I would not casually allow one into a game.