^^^^^^^^^^X3 However, that doesn't quite explain why your wheel cover doesn't fit. If your Lincoln wheel covers have the conventional claw like grips around the perimeter of the cover, there has to be some interference between the wheel and the cover. Suggest you look closer and perhaps use some play dough (or dabs of wheel bearing grease) at the suspected or potential interference points and check for evidence of contact when fitted.
Since the consensus is Dodge, that would explain why they don't fit. The raised center of the hub sticks out too far and hits the back of the cap. So, IN THEORY, if I were to "update" to the correct 15" 1951 Ford wheel the caps should fit? Ugh. EVERYTHING is backwards, thanks Grandpa Al! Hahaha
I wouldn't be so quick to think the stock Ford wheels would work any better than the Dodge wheels you have there. It isn't that they are Dodge wheels per se, it has to do with the 'front spacing' of the wheels...same for the '51 Ford wheels. There are both Ford and Dodge wheels that are deep enough to accommodate your Lincoln caps. I'd look for wheels that have a bit wider rims as they are more likely to have more 'front spacing'.