Train ticket

what do you intend to do at Zermatt and in Luzern?

When is the trip?

I can see an emoticon after your question but it is one I have never seen before so have no idea of its meaning

This is relatively easy though not straightforward simple:

Buy on Trenitalia (www.trenitalia.com) an advanced ticket Milano Centrale - Luzern. They have 2 or 3 direct trains per day that can be sold online as little as €29 one-way per person with enough advance (cheaper tickets disappear faster).

Buy a Saver Day Pass on SBB (https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/1-day-travelpass/saver-day-pass.html) for the day on which you will travel from Luzern to Zermatt. Tickets sell as little as CHF 52 per person when bought as soon as made available (exactly 60 days before intended travel). A Saver Day Pass allows unlimited travel on almost all Swiss trains, including all sectors you need to go to Zermatt. Actually, you can take the scenic route via Büring (the so-called Golden Pass Line) without paying anything extra, and can also take the slow scenic route to Visp via Kandersteg (no extra charge as well). Or you just take the fastest trains. In any case, a Saver Day Pass is cheaper than stand-alone tickets.

For the return Zermatt-Milano, it is a little trickier: (1) find suitable travel times all the way Zermatt - Milano Centrale on www.sbb.ch/en. There are several options (the fastest ones) with one transfer in Brig or Visp only (and not further transfers in Italy at Stresa or Domodossola). Leave this screen open. (2) go on www.trenitalia.com and search and buy the Brig (or Visp)- Milano train there. It will cost as little as €19. (3) buy a Zermatt-Visp (or Brig) train ticket for the day of your travel. There is no need to buy this ticket in advance. You just need to make sure you catch any Zermatt-Brig (or Visp) train that arrives before your international train to Italy departs. SBB will suggest tight 7 minutes connections, I'd say search for trains arriving 30min before because of split ticketing. Search this connection Zermatt-Visp/Brig online (on SBB) on day of departure and leave earlier in the unlikely event there are delays on the route so that you make it on time to Brig/Visp.

Zermatt-Milano alternate: if you find the above instructions too cumbersome, you can search for "International Saver Tickets" on SBB for the whole Zermatt-Milano sector. They will sell tickets for the same trains you'd get on Trenitalia, but at much higher prices.

Trenitalia won't find "Zermatt" on its online system. They only find Swiss stations where trains to/from Italy call at. SBB online system will find Italian stations where international trains from Switzerland operate.

That seems a little complicated, but is the the cheapest way to get the best trains you want for your itinerary. A Swiss Pass is totally not needed in your case, nor does a Half-Fare pass make any sense either.

All these tickets are online, no need to pick-up or print anything.