What is the prison meaning?
The semantic space that "lager" covers in German is around storage/collection: so it covers concepts that in English are distinguished by worlds like "camp" (storage of people; and is therefore applied to prison camps) and "warehouse". Lager beer is matured in cold storage (like a cellar), hence "Lagerbier" just means "beer kept in storage", roughly. Because of differing semantic coverage, a lot of words between Germ…
It's wider than that and covers also the sleeping place of people and animals. Lager is related to lair in English.