That's funny. We did 3 nights in Barcelona after Lake Como and Milan. On that travel day, we left our hotel on the lake around 8am, took the ferry and train to Milan (arriving into Milan around 10:30am), stored our bags at the train station, and went by Metro to see the Last Supper and the Duomo. Then we picked up our bags, took the bus to the LIN airport, and flew out on a 5:45pm Alitalia flight to BCN.

Since your 11:15am arrival into Milan isn't a redeye flight, you should be mostly rested upon arrival. You could do pretty much what we did if Last Supper tickets are available, and then take a 2-hour train to Venice or Florence at the end of the day.