I didn't see any updated information on the travel forum regarding obtaining Last Supper Tickets, so I thought I would share my recent experience. As others have said, touring companies buy all of the tickets as soon as they come available. I went online that day and they were all gone. On this forum, I read some people obtained tickets by calling. I tried that and got a recording in Italian I didn't understand. However, I kept checking the website and noticed that tickets were available for days that before none were available. I came to the conclusion that when touring companies returned tickets they couldn't sell, they were put back on the website. Checking the website almost every day, I finally got tickets for May 28th today (May 6th). Also, they are extending the viewing times until 10 PM, because of the World's fair in Milan. So far they have put the extra times on the website up to May 18th.
One tip - you will need to register as a user on the Vivaticket website in order to get tickets. You can do this before your tickets become available. I selected my ticket time and then had to register and somehow lost my place. When I logged back in, my tickets were gone (probably being held for me from the first time I had logged in). I waited an hour and went back in to get my tickets.