You may need a custom brake kit
I subscribe to Auto Restorer magazine and read the two-part article on front brake disc conversion in the September and October editions. I am restoring a 1955 Lincoln convertible and cannot find any sources for kits or technical
advice on a disc brake conversion for my uncommon vehicle.
I am not aware of a bolt-on disc brake kit for your 1955 Lincoln. If you wish, Master Power Brakes (mpbrakes.com) will produce a custom kit for you. This requires that you send your spindles and related parts to Master Power. They would do the necessary machine work and other modifications to your original parts and add in all of the necessary new parts. What you’d get back would bolt right onto your car.