Milan to Lauterbrennun

It all depends on the specific time hour and day you leave if you specify that you will get an exact answer.

I see a better way that you can go to Spiez direct on Trenitalia from Milan.
Then you take the Swiss Rail to Interlaken and then to Lauterbrunnen.

To start with, go to www.sbb.ch/en and put in your date and from Milano Centrale to Lauterbrunnen. Start at 6:00 am and you can page through all the possible trains that will get you to Lauterbrunnen that day.

if you want to go the easiest way, take one of the EC trains going to Basel or Frankfurt. There are 3, at 7:23, 11:23, and 18:23, those trains will go through Spiez, where you get off. and proceed on the next train to Interlaken Ost, then get on a train to Lauterbrunnen, checking the carriage you board that it is indeed going to Lauterbrunnen (some go to Grindelwald when the train splits along the way).

So the easiest thing for you to do is decide which of those trains you want, and then purchase a ticket now, to get a discounted train specific fare to Domodossolo. It will come with a seat reservation. At Domodossolo, a Swiss train crew will board and take over operation of the train. Show the conductor your Swiss Travel Pass, and that is it. You can buy the ticket at www.trenitalia.com or www.trainline.eu