One Day Trip from Lugano By Train

Just go to www.sbb.ch, look up "Lugano Paradise" to "Milano" and you will find times and prices. But enquire if your hotel gives you the Ticino ticket, as that covers all public transport in the canton. In that case you only would need to add a ticket Chiasso - Milano.

I think the answer to your question depends partly on what you want to see and do in Milan vs. what the organized tour includes. Rail service is so convenient that I don't think the intercity-travel component of a bus tour (or even a tour that travels to Milan by train) adds much value, and travel by bus might be slower.

An issue I have with bus tours that make a bunch of sightseeing stops is that they, not you, determine which places you go and how much time you will spend at each place. I've observed tour groups in museums; they spend much less time at those museums than I would, being an all-or-nothing sort of museumgoer. I think bus tours that include indoor sightseeing (not all do so) are usually best for folks who prefer quick visits to a bunch of places, unless they go to places difficult to reach by public transportation. Milan has excellent public transportation.

My time in Milan was focused on art museums and the Duomo. Even the Duomo and its roof were easy to get tickets for last summer (though that should be checked in advance). There may be an extra experience (maybe climbing the dome?) that is a much harder ticket to get. However, the really tough ticket in Milan is The Last Supper, which sells out very quickly (in minutes, I think) when online tickets go on sale. I think it's extremely unlikely a bus tour from Lugano would include a visit to The Last Supper. That's a ticket you'll need to arrange yourself, if you want to see it. (There's info in other threads here about ticket-purchasing procedures.)

In summary, I don't think Milan is a destination for which it's very helpful to take a bus tour from Lugano. Perhaps someone has actually done that and can provide better information.