One Sunday, June 4 we are taking a guided tour of the Milan Cathedral that ends at 4:00. We have a cooking class that begins at 6:00 located at Via Vincenzo Foppa, 20144 Milano. If we are able to get tickets for the last supper on the official website at 4:45 would we be able to make the cooking class on time? Also, would we be able to travel from the cathedral to the Last Supper to make the 4:45 time slot?

rome2rio gives you an idea or google maps gives walking times

In theory, the timing all works. I would arrive at the Duomo well before the tour and use the time to really look at the architecture, the decorative elements, walk the perimeter, then briefly walk through the interior. If the tour doesn't include the roof, I'd do that as well. The tour might not give you time to linger much anywhere, and you really must leave the Duomo at 4:00. You need to arrive for the Last Supper before your reservation time, and I'd want to be there no later than 4:30 for a 4:45 reservation. Your viewing time is limited to 15 minutes.

Both times we went to The Last Supper we had to sit with the group in a contained area to be dehumidified for 15 minutes before entering the area where The Last Supper is for another 15 minutes. So you need to arrive more than 15 minutes before your reservation.

Your group will be taken to a room 15 min before your s heckled time to see The Last Supper. We were told this was to dehumidify the group prior to entering the church of Santa Maria delle Grazia where The Last Supper is located.