Carbide Die Service started producing Lifetyme carbide dies not long after WWII. Carbide Die Service was the name of the company, and Lifetyme was their brand name for Carbide sizing dies. Seems unlikely that Carbide Die Service would have produced a Steel die, and if they did, it wouldn't have been called Lifetyme.
I know they applied for a Patent, as I have seen Lifetyme dies with a Pat. Pending stamp. I have never seen one with a patent number, and a patent search came up empty, so someone else must have come up with the idea first, but maybe didn't commercialize it.