I think you'll probably need to hunt one with your engine information instead of the Lincoln information. Maybe someone on here knows what power unit Lincoln used in that model but I don't. If you get the power unit information complete as possible I think it should be relatively easy to get a mag. Good luck.
I used to have one of those that was powered by a single cylinder Kohler engine. Don't remember the model, I sold it since it was a screamer (3600 rpm). Some photos of yours would probably help someone identify it as well.