Re-edited due to aging brain cells.......!!!
Lee,
Hit up your local FIAT enthusiast....if there is such a thing......!
You might try working backwards from the key blank......"What does it fit?" Sort of thing and then....cruise the Fiat web boards for lock assemblies or even pins......
You can also probably try reaching out to Roland in Germany for bits and pieces like this! The push button design was used in the FIAT 850 SPYDER models from what I can tell from limited looking. I wish I would have grabbed every one of those locks that I walked past.......along with 68 Mopar side marker lamps.......!!!!! Shoulda woulda coulda.....! 
There are lock sets offered up for sale, by Bayless and Mr Fiat, but these morons fail to list what years..... Pictures show a rectangular shaped lock assembly....NOTHING like what you see on pictures of 65-72 850 Spyders (Spiders)!!!!! Perhaps they expect you to cut the crap out of your car to fit them......
What I also noticed is that MANY of these cars seemed to use a double sided key blank.....on 124 models of many years, and also the 850 sedans. Whether the lock pins are the same.....can't answer that at this time. You would need to verify the key # for fitment.
OK, much better than my start on this reply!
Good luck!!!!