M!ke, does the pushbutton on the passenger side deploy as deeply? Otherwise, this is probably just an alignment of the chrome valance. Under that chrome is the sleeve that guides the cylinder--the fit of the sleeve in the door sheet metal itself is pretty tight, and the fit of the cylinder itself should be tight as well...The sleeve is what should provide alignment to the chrome surround. I suppose somehow it may have shifted after 51 years---even though the mounting for the chrome is also pretty snug, you may be able to just slightly budge the chrome (so the cylinder doesn't get trapped behind the chrome).
Behind the cylinder is that latch, which was used on Alfa Spiders and Lancias for a few decades next... but see that arm that the cylinder pushes on is really stout, and unlikely is causing the problem here. So if the travel on the driver's side is the same as the passengers, and if there is no play up and down between the cylinder and sleeve, should just be a matter of aligning. There just cannot be much more that would go wrong, very little in the stackup here...But if really a nuisance, a little shim in between the arm and cylinder end (so that the pushbutton won't go so deep as to get stuck behind the chrome) and you are done...
(Steve, btw, except for the latch, the key and cylinder appear common with Alfa Giulia sprint (trunk) and of course the chrome pushbutton bezels with Pantera--but I haven't found any other use for the cylinder or the sleeve. Luckily, I have mine--but I was curious and looked and looked w/o succcess...Fiat 1100 trunk may be close, I'm assuming my set came back from being re-keyed (!) so have lost interest in buying from Ebay Italy to find out...!) Lee