There were lots of things that suggested Luthen was a Jedi of some sort, most importantly his monologue to Lonni which now after he's been given a backstory so doesn't fit the character that the most logical explanation is that it was all an act to keep Lonni on board. The truth is, Luthen had given up nothing to become what he was. He'd already lost everything before he started fighting the Empire. He was already a broken man before the rise of the Empire back when the Empire's only atrocities were just cleaning up and suppressing separatist holdouts brutally. The reality given his backstory is that becoming a resistance leader gave his life purpose and meaning that it had lost. He was suicidal before that point, it's not like he had to give up anything to do the job. So he made up something that Lonni would believe in just as a trick to keep Lonni trusting him. Only that makes him despicable and not heroic. It turns him from an anti-hero to an anti-villian - someone who just happens to hate the Empire, not someone who actually loves good.
Luthen's reveals ended up completely undermining who I thought he was as a character. I suddenly became very sympathetic to the Alliance leadership that wanted little to do with him. Murdering Lonni and then turning out to be just a broken disillusioned NCO who embarked on a life of vengeance to somehow redeem himself for his role in the Empire's genocides seemed as you say to not quite fit. The only way to make it fit was make it an act or else to leave out all the really important aspects of his life which is just bad story telling.
Why did a sky kyber crystal have special meaning to him? Why the walking stick he never really uses if it's handle just contains an ornate blade? The red lightsaber like beams aren't really to me a big clue, because we know that Republic gunships use similar lances as anti-personal weapons so they don't have to be Jedi tech. But why is he one of the foremost archaeologists in the Galaxy, if he's just an NCO for crying out loud? People from wealthy scholarly backgrounds rarely end up as enlisted men. How was he able to emulate the elaborate mannerisms of an inner sphere courtier? The background fit so little into what they had shown that it felt to me like it was wrong.
I'm fairly sure the reality is that he was meant to be a Jedi in season 1 just as originally Lyra Erso was meant to be a Jedi in Rogue One, and in both cases Tony Gilroy backed out of that because they wanted to highlight the role of "normal people". And sure, you can do that, but I think you need a better back story as to how this guy was one of the foremost archaeologists and antiquitarians in the entire galaxy than he was just some NCO with PTSD.