Train from Turin to Lugano

I can find available scedules with one stop at Milan Centrale.

I doubt it, you will in all cases have to change trains at Milano Centrale. And both trains will make other stops between Turin and Milan and between Milan and Lugano.

You don't say when you are travelling (28th of which month, and that could be the key. Tickets are only available a few months in advance, and Trenitalia (Italian Railways) have so far only published times up to June.
I looked on https://www.trainline.eu/ for 28th March and saw lots of trains with prices.
Beware, Trainline also list buses.

I also looked on Trenitalia ( https://www.trenitalia.com/tcom-en ), prices there start at €12.45, a good price.
Tickets are a lot cheaper if you buy them in advance on the internet, you then get e-mailed a "self-print" ticket which does not require validating. Many of the trains listed are NOT regionalle, so no validation anyway.

You probably need some sort of ticket for your dog, I don't know what. If you want more time in Milan, I suggest you do two separate purchases, I can see no way on Trenitalia to specify a longer interchange time.

Looking at trainline.eu Torino to Lugano on Friday December 28 (your question is not clear so I assumed this date) I see prices and the cheapest are highlighted:
https://www.trainline.eu/search/torino/lugano/2018-12-28-10:00

Don't worry about buying the regional train in advance since the prices are fixed. Buy that ticket at the train station.
You have 6 hours from the time you buy the ticket to catch whatever route you bought.

Chris F
Sorry, wrong lingo, meant one connection, not stop.

Will arrive in Milano on Monday, Dec 24, then go to Turin, dec 25th, then Lugano on dec 28th.

Italo doesn’t work as they charge $50 per ticket for a dog. (Unless Trenitalia was more than 100 pp) Trenitalia is 50% off adult fare.

I searched for trains after 10 . And want to arrive no later than 3-4
10:54 RV Torino to Milan (trainline says no price found) RE Milan to lugano
11:50 frecciarosasa/RE. Not available - does that mean it’s sold out?
11:54 RV to Milan / RE to Lugano- no price found. Trenitaila and SSB both say not purchasable on all the regional trains

Still don’t see any prices for Trenitalia RV/RE combinations, would just like to know for our budget. I know the prices don’t change on regional trains, but it’s nice to arrive at station and have tickets in hand and not worry about lunes ar machine or window. And if the frecciarossa trains are less we’d purchase those. .

This morning I came within 30 seconds of missing my train from the airport. The ticket machine only showed a child ticket, and didn’t even give option to purchase. Went to ticket line which went quick, but way too close for comfort.

I searched by torino to Milan and see price for regional train for 27.90€.
Assuming this price will not change between now and Friday
But when I search for Milano to Lugano, EC (euro city) trains show price of 24€ But no prices for regional trains.

Are Eurocity trains for a specific train and time once tickets are purchased?

I searched the Trenitalia site for regional trains on the 28th and it seems they are sold out. The faster trains are available but some of them are sold out as well.

I searched by torino to Milan and see price for regional train for 27.90€. Assuming this price will not change between now and Friday

That price may change and it sounds like you are looking at the price of a long distance high speed train the Frecciarossa that goes all the way to Rome and not a Regional. The regional trains Torino to Milano are set at 12,45 € and take 1 hour and 52 minutes. Those regional train do not officially sell out as there is no seat reservation. You have to search using Torino Porta Nuova as your departure station or Torino Tutti Le Stazioni

Are Eurocity trains for a specific train and time once tickets are purchased?

Yes, for Eurocity trains originating in Italy there is a set seat assignment and time.

But when I search for Milano to Lugano, EC (euro city) trains show price of 24€ But no prices for regional trains.

This route is also operated by TiLo-Regio https://en.wikipedia.org/wiki/Treni_Regionali_Ticino_Lombardia.
You can only see the price or buy the tickets on SBB site and those are selling at 28CHF on December 28
https://www.sbb.ch/en/home.html

We bought the tickets today at the main Torino train station for travel tomorrow. The regional train from Torino to Milan was €12.45 and were able to buy our Cane (dog) ticket for half price. For Milan to Lugano - 2 adult tickets (€13.00) for the regional train, but unlike regional trains in Italy, our reservation for the Swiss train is specific for that train. So we allowed an extra hour between trains. And we have to purchase the dog ticket once on board by looking for the conductor to pay half fare.

Just a reminder to validate before boarding trains in Italy. We purchased the tickets the day before for our trip from Milan to Turin on Tuesday. So we we got to the track and boarded the train, and didn’t realize till about 10 minutes later that I had not validated. So walked toward the front 2 cars, found the conductor, and told her I forgot to validate. She was very pleasant and hand validated and scanned our three tickets. Close call!