I agree that it's not a just New World with a Lincoln badge - the frame is too different from the New World Tourist. I hesitate to call them a "lightweight" because the frame might be a diamond, but it's heavily constructed like ballooners or antique type bikes.
They remind me a lot of the kinds of bikes that were made before WWII for Western Union and similar businesses or local government - built like an adult bike with a diamond frame, but heavily constructed similar to an antique period bike or early ballooner. With the weird, low serial numbers, I wonder if these are part of a smaller run of bikes made for a business that used bikes, or some kind of local government/police where a small fleet bikes would be used.