<<"What we would really like to do is leave our luggage at train station hike to an inexpensive hut spend the night and hike back to our luggage.">>
Many medium to large sized stations stations have lockers or left luggage offices. Many small and unmanned stations do not. The list of stations on the SBB web site describe such services and such equipment for each station, after you find the station on the site:
Lockers are under "Equipment"
I don't have any personal experience doing the kind of hikes/accomodation that you describe , so we'll have to see if others can jump in.
If I were to try to do that for my self, I'd have to do some serious exploring to figure out ideas. Here is what I would do. There has to be a better way...this is hard work. ;-)
My first step would be to look at different routes into Switzerland and on to Luzern from Italy, to get ideas about timing. I know how to go by the common routes from Milano, as well as through St. Moritz. To go to Luzern, the links provided above can give a start.
If you are coming from Monterosso in the Cinque Terre, the time table shows default routings ( default is fastest route) . I have attached a screen grab showing the first 8 journey options after approximately 0700. All have changes, a many as 4 changes, as few as 1 change, and take from 7 1/2 hours to 9 hours, approximately.
My next step would be to click on the "+" sign to the left of each journey to study the routings and gain more details.. I'd then compare them with the map linked above to see how the route. Also, after I open each set of journey details , I find a map available in the footnotes, showing the routing. I also can find intermediate stops.
When I do that for each of the 8 journeys shown on the screen grab, all go through Milano Centrale.
The first journey would get you to the Swiss border at Chiasso somewhere around 11 AM, and to Arth Goldau at 1343. I'd look along that part of the route; the part from Arh Goldau to Luzern is less scenic, although day hikes certainly would be possible, I'm not sure where I would look for hostels. Certainly no SAC huts. Between Chiasso and Arth -Goldau, or more likely between Belinzona and Flüelen would be mountainous regions with some well known hikes in/above the train and road routes through the passes. There are no train stops shown in that region. So, I'd have to look at bus routings, and the narow gauge line that runs back up to the Gotthard from Göschenen toward the Furka Pass. Not a lot of time in that day for any serious kind of hike, even with an early start from Monterosso.
So, my next step would be to try to find hostels or other accomodations along that portion of the route. I have never tried to do that, but, I would start by looking at the individual towns on the internet, and by checking Switzerland Mobility to see what trails might go through the area, once again searching by town name for a start ....if you find a trail in Switzerland Mobility here, it will list accommodations along the route.
www.wanderland.ch/en/h iking-in.html?phrase=+Gotthardpass+% 28TI%29+-+Airolo&sname=&sid=199 168
The process that I have described is extremely time consuming.
But, if you can narrow down your request as much as possible, try posting in the Accommodations section of this Forum.
Your best bet is to find someone who knows the area(s) who will jump in. Perhaps the forum moderators (Arno and Annika) can help to refine your search. That can reduce the time needed on the search. The way I describe is not very efficient, but it all I can think of, and, it has some chance of working. And, it lets you see the kinds of tools that exist for trip planning.
There is a section on this website on inexpensive accomodations, also: