Beavers do live in lakes, and they even build structures out of wood to live in there. Those structures however, are "lodges" however, and not dams. Beavers do not live in dams. Beavers build dams to make a lake or pond, and within that, they build a lodge to live in. (If a lake would be there anyway, chances are beavers wouldn't bother to dam it up further)