Lucerne to Milan Central using Swiss travel Pass

You can purchase from www.sbb.ch/en Luzern -> Milano Centrale. You can also choose to reserve seats if you wish or just let the website determine if you need or should reserve them. You can specify that you hold a Swiss Travel Pass, and the appropriate price will be calculated for you. The only credit card that ever works for me on SBB is my Amex. Good luck

Tim has guided you well. Just adding that it is not a non-stop train, but a direct train. It will stop various places but you do not have to change trains.

This train IS NOT non-stop. There are no trains on this route that are non-stop. It has many stops. What it is, is a direct train, i.e. no changes required.

"What is the best and fastest way to reach Milan Central station from Lucerne USING SWISS TRAVEL PASS TO THE MAXIMUM." - this or any other train from Luzern to Milano Centrale. Some trains are direct (like this one), most require a change. It does not matter which you choose, they all take the same route and the same time.

You do not need to reserve seats on this train (or any other) in Switzerland. You DO need to reserve seats if travelling on it in Italy.
Your Swiss pass is only valid in Switzerland, up to the last Swiss station the train stops at (which is Chiasso). You therefore need to buy a ticket from Chiasso to Milano Centrale for this train. This ticket will include the reservation.
You can buy this at the Trenitalia website: https://www.trenitalia.com/en.html
You will not need to get off the train in Chiasso.

List of stops for train EC151
Luzern dep 12:18 EC 151 EuroCity
Arth-Goldau dep 12:50
Bellinzona dep 13:51
Lugano dep 14:22
Chiasso dep 14:51
Como S. Giovanni dep 14:57
Monza dep 15:23
Milano Centrale arr 15:35

Thankyou Tim/laurel and Chris,

My apoligies for the wrong choice of words..I also meant a direct train without any changes .
It appears from the SBB site,that the ticket charges of the EC trains from Chiasso to Milano Centrale,are nearly double than the other trains.

Do the train station(say Chiasso or Lugano) have lockers at the train stations where one can keep their luggage, then spend some time in the city sight-seeing or just to take the later/cheaper train to Milano Central

Lugano has lots of lockers, both small and large.
https://www.sbb.ch/en/station-services/railway-stations/lugano-station.html

Chiasso has fewer lockers, small and large.
https://www.sbb.ch/en/station-services/railway-stations/further-stations/station.5307.chiasso.html

You said you wanted a direct train (no changes) and the easiest way to do that is to buy the ticket from Luzern to Milano on the EC 151, entering your Swiss Pass for a reduction. You can do this on SBB.ch, where the total charge will be 20 CHF, or on Trenitalia, where the charge will be 17 euro.

Or you can book the EC 151 just from Chiasso to Milano for a Super Economy fare of 9,90 euro, and use your Swiss Pass for the portion from Luzern to Chiasso. I assume it is OK to split your journey in this way, but we have never done that.

The cheaper tickets from Chiasso to Milano (5,50 euro) are for the regional trains. You would have to get off the EC 151 and change trains, waiting for the next regional train. Seems to defeat the original purpose of taking the “fastest” train to MIlan. And if you put your luggage in a locker in the station, that will cost you.