What was Thomas' background?

We don't know.

Arguments For:

Certainly Lore treats him as such as soon as she sees his concentration camp tattoos, regardless of his fake papers (which she later learns about). This explains her behaviour at the end of the film. Whilst he was using a dead Jew's papers, it is a jump to go from learning his papers are fake to believing everything about him is a lie. Using fake papers would still have been easier than having no papers at all, which seems to be the only alternative.

He is a survivor - both of the camps and beyond. Once leaving, and without any papers, he continued to adapt, doing what he had to to survive - including taking the dead man's papers.

He does tell the young boy that he isn't Jewish, but it could be argued this was to avoid scarring the boy anymore - the ideas of Nazism he had were his parents, not his.

This also brings a nice full circle to the story, with Lore ending up trusting the person she was taught to hate. Thus in the film there's a strong logical argument that he is Jewish.

Arguments Against:

The director, Cate Shortland, revealed that even Thomas' tattoos were fake:

Interviewer: [Thomas] could have been an SS man himself for all we know.

Cate: He tattooed himself. That tattoo is not from Auschwitz. I loved that – that everything is slipping through your fingers, in Germany in 1945. Nothing was real.

Knowing that changes things. If those tattoos aren't real and his papers aren't real, then suddenly things seem very different. To me, it suggests he was an SS guard. That would give him intimate knowledge of the concentration camp tattoos, knowledge of the camps and access to papers and knowledge that posing as a Jew would have been less dangerous than in his real guise.

It also presents a wonderfully wicked irony to the story - Lore learns to question and disagree with her parent's bigotry through a man she believed to be Jewish, who was in fact everything her parent's bigotry represented.

Conclusion

Consider the meaning of the word lore: a body of traditions and knowledge on a subject or held by a particular group, typically passed from person to person by word of mouth.

The main focus of the film is Lore's changing beliefs about the world around her, from her parent's authoritarian and narrow minded view, to one of her own. "Thomas", whoever he is, proves to be a massive part of that.

His true identity is a mystery. But the fact he helped open up Lore's mind (either as a Jew, a regretful former guard or a guilt free former guard) isn't in doubt - and that's the message the film maker wanted to leave us with. Don't question his background - question her transition from one way of thinking to another.

It is more likely Thomas is a kapo rather than a Jew or guard.

He is able to commit serious crimes easily and without real reason. His actions are more of a serious criminal possibly psycho rather than an SS guard.

He is more likely to have been a serious criminal transferred to the camp by the Nazis and made a Kapo who's job it was to lead and make life harder for the Jews.

This way he would have been tattooed and would have had access to papers.

I don't think he was a Kapo, a hardened criminal would have taken advantage of the girl, and probably would not have bothered to help the children.