Is the problem here that the nut is missing or simply that the lamp is broken?
Unless the OP is trying to do some sort of "authentic" restoration of this lamp, maybe it would be easier to just replace both the pipe and the nut with parts that are standard and available.
But that would mean that whatever (probably) screws onto the other end of the pipe probably wouldn't fit the new pipe. So, maybe it would be possible to cut off the end of the pipe that mates with the missing nut and attach (weld, epoxy, Loctite, braze, solder) a new end with standard threads.
Maybe.
-- Russ