I know this is an old thread but I'm just reporting in on my experience. I had the dreaded sticking door button on my 156. The button wouldn't pop out on its own, I had to wiggle the key in the lock to get it out. I tried WD40, brake cleaner, silicon grease, no joy.
So I bit the bullet and followed the instructions on alfa156.net for stripping the door and removing the handle. The instructions are pretty good but it still took me a while, the biggest challenge being getting the linkages free before removing the handle from the door.
Instructions again: Fun starts @ 3000!
Eventually I got the handle assembly out and was able to split the lock from the handle (3 small screws). It turned out the cause of the sticking wasn't accumulated gunk, it was a rubber o-ring at the base of the button that had split and was getting trapped between the button and the barrel, preventing the button from popping out.
I gave it all a good clean and grease and then re-assembled without the o-ring (because I didn't have a replacement). All good, the button now works fine again. I know I'm storing up trouble by not having the o-ring, as presumably it's there to prevent gunk getting inside the barrel, but I also now know how to strip a door!