I recently had an 8:50 AM flight from Malpensa to Munich connecting to LA (United ticket, but these were Lufthansa flights). I arrived at the Lufthansa counter at about 6:45 AM and was the only one there. Checked myself and my bags in very quickly and then had two hours to kill, mostly before the restaurants and shops were even open. So in my experience, three hours was not needed. A little later in the morning and if your flight is directly to the US, it might be different. I spent a fine last night at the First Hotel Malpensa with nice rooms, good rates, free airport shuttle ride of under 10 minutes, and they serve breakfast beginning at 6:30 AM. You might spend the day and even have dinner in Milano with your bags stored, then catch an evening train to Malpensa, and then have a more leisurely morning before your departure.