The existence of Forlong the Fat at the end of the Third Age is our only reference to a Lord of Lossarnach, so we have no way to be sure how far back the title extended into history. It might in principle have been as old as Gondor itself, or perhaps even older, but we have no way of knowing whether Forlong was a descendant of such an ancient line.

We might expect that the Lord of an important region of Gondor bordering on Minas Tirith would be descended from the Dúnedain, and indeed this might very well be the case. It is curious, though, that Forlong's name comes from the pre-Númenórean language of the Men who occupied the region before the Dúnedain settled there (whereas the names of the Dúnedain are more usually derived from Elvish). This is hardly conclusive, but it suggests that the Lords might have been, at least in part, descended from the population who had lived in Arnach before it became part of Gondor. If so, this would make their line very ancient indeed, dating back into the Second Age.