[tubman]

Take a closer look at the pictures. If you compare the disc as cut with the picture of the assembled piston, you can see how the deep piston is recessed to hold the disc (on my Mallory anyway; I would expect a Ford to be about the same). This is also why you have to have the thickest possible leather for this. Any wear on anything much thinner would put the metal piston in contact with the metal rim.

And yes, these should be saturated with lubricant before or after assembly. I would expect Ford used regular motor oil, but there have already been a couple of other suggestions here. Some may work better than others. This oil impregnation is one of the reasons glue is not used with these, either to attach them or make a leather laminate.