Is there a direct train from Lugano to Malpensa Airport? If so, what is their website?
https://www.trenitalia.com/en.html
A couple of direct a day or change at Gallarate
Don't bother with Trenitalia, www.sbb.ch/en will show all, and you can buy tickets there. The trains are called TILO trains, as they are a joint venture of the Swiss canton of Ticino and the Italian province of Lombardy. I believe that currently the only direct train is at 5:06 am. Otherwise, there is a train change in Mendrisio. But beginning August 31, there is a direct train every hour at 6 past the hour. Cost is 25 CHF, 2nd class.
The same train looks to be direct on Trenitalia and needing a change in Mendrisio on SBB. The mistery is explained: there are two suburban TILO lines from Lugano, S10 to Como and S50 to Malpensa. They travel coupled to Mendrisio where the train is divided in two sections, one going to Como and one going to Malpensa. So be careful to which car you board and you can go directly to Malpensa.
Well, there is another catch: if you get out at Gallarate and take a direct train to Malpensa you can arrive a few minutes earlier than staying on the S50 train that takes a longer detour to the airport.
Believe the S10 trains are all direct, just a bit over an hour. We did this on the way home last year.
SSB app best place to book, likely have this loaded as you have been in Switzerland. Note T1 or T2 stop.