"He lives in peace."
Translation:Er lebt in Frieden.
You are asking whether the preposition "in" requires an accusative or dative definite article, and the ABSENCE of the article is what you should be focussing your attention on.
Abstract nouns are not accompanied by an article when they denote qualities, states or processes. However, abstract nouns of this kind are accompanied by the definite article when what they refer to is in some way made definite by the context. We are not discussing THE peace, a concrete event, but rather peace as an abstraction here. Hence, there is no article after "in".
I don't quite agree... I would go for the explanation of a fixed expression, because it looks like abstractions in German do very often pick up definite articles: https://forum.duolingo.com/comment/12391597 https://forum.duolingo.com/comment/22553798
Edit: People seem to use "im Frieden" too, and some dictionaries have both forms.