Train from Milan to Lucerne

You can always just buy a train ticket. How do you think 98% of the riders get on the train? And usually, you will get a better deal.

There is no train in Europe that requires a Eurail Pass. There are plenty of trains where an Eurail Pass is not valid though.

On the subject of passes: What are your plans in Switzerland. Do you need more train travel than just Florence - Luzern? And when will this be?

To Green Bay
Maybe I didn’t ask the question the correct way
But the tone of your answer was unnecessary
Yes I realize one needs a ticket
What I was asking is if I also need an Euro pass
Is it mandatory

It's called a Eurail pass. And it is never mandatory. And it rarely will save you money over buying tickets from the train line in whatever country you are in.

However, the question about your travel plans within Switzerland was a valid one, since there ARE Swiss passes that can save you money there.

You never need both a ticket and an Eurail Pass, as the Eurail Pass replaces a ticket. The Pass is the ticket.

In order to travel by train you always need either a ticket, or something that is equivalent to a ticket, as for example an Eurail Or Interail or some local pass. A ticket is a proof that you have paid to be transported, usually along a particular train route, or in the case of a pass, a whole network.
On top of a ticket you can also get a reservation. A reservation gives you a guaranteed seat. Some trains do not let more people on board than there are seats, so for those trains you must get a reservation. So if you have an Eurail Pass for those trains you need to get a reservation in addition.

And here is where the Eurail Pass is not so convenient. In Italy reservations are compulsory for long distance trains. So if you have a Eurail Pass you still need to go to the ticket window at the station to get the reservation. Tickets however you can buy on line, or using your phone, or at a travel agent, or from a ticket vending machine, and they will have the compulsory reservation included at no extra charge. Which is why an Eurail Pass is not very convenient in Italy.

Florence to Luzern currently the best way to do this is to book this on www.sbb.ch, the Swiss Railways, as Trenitalia has issues with selling tickets for Switzerland. In both cases the trains you will take will be Italian ones till the border, and Swiss ones beyond that.