Lake Como

From Varenna you need to go back toward Milan, get off at Monza, then take a train directed to Zurich, get off at Arth-Goldau, and finally take a regional train from Arth-Goldau to Luzern. So you need three trains for a total of about 5 hr journey.
Not sure what to tell you. That's the only way from Varenna.
The other option would be to stay closer to Como, and catch the same train from Como (instead of Monza). Or you can stay in Menaggio, catch the bus from Menaggio to Lugano, and catch the train from Lugano. However I don't think the bus from Menaggio stops exactly at the Lugano train station.

Betty,

The most direct way to get from Varenna to Lucerne is to return to Milano Centrale (1H:03M) and then connect with trains to Lucerne. The travel time from Milan to Lucerne will vary depending on which train you choose. One of the shortest travel times is a departure from Milan at 10:25, arriving Lucerne at 14:20 (time 3H:55M, one change at Arth-Goldau, compulsory reservations on first segment).

The next departure with that travel time leaves Milan at 12:25, arriving Lucerne at 16:20. There are numerous departures to choose from on that route.

It's a very straight forward trip, and that's the route I'd use.

Have a look to a map. The lake has an inverted Y form, with two branches separating at Bellagio, and it is surrounded by mountains. There is a railway line along the east cost from Lecco to Colico - Varenna is roughly in the middle - this line goes north to Sondrio and Tirano, and south to Monza and Milan.

There is a second railway line just touching the west tip at Como - this is the international line Milan, Monza, Como, Lugano, Gotthard tunnel and north to Zurich and Lucerne. - There is also a third local line to Milano on a different itinerary. These are your railway options. Out of those options, you need buses or ferries. There was once a railway line from Lecco (east tip of the lake) to Como (west tip) but it was so slow that in the end it has been decommissioned as going back to Monza is faster.

The geography being this, if you want fast access to the Lucerne line, you need to stay in Como or anyway a place not so distant from Como. If you want to stay in beautiful places like Bellagio and Varenna, you must bite the bullet and live with the inconveniences of transportation in Alpine and sub-Alpine regions.

Some railway tricks; if you stay on the east coast, there is no need to go back all the way to Milan; you can change trains in Monza, where the railway lines separate. Monza is also a smaller station and easier to navigate. In Como, you need the Como S. Giovanni station that is somewhat elevated and distant from the lake shore, so maybe you need a taxi to reach it. Sometimes you can better take a regional train from Como to Chiasso (10 minutes) - Chiasso is already in Switzerland and may have more trains than Como to the north of Switzerland. Also, there is a railway tunnel detour around Como and some long distance trains run the detour stopping in Chiasso but not in Como.

Thank you all for your detailed and informative response. I am officially 'put into place' with comment from Lachera - anything worthwhile does take some effort! I have some decisions to make.

I took the train from Milano Centrele to Luzern (Lucerene to some) and we had several nice lake views once we got to Lake Lugano and then the lower end of Lake Lucerene.

I see Trenitalia routes you Varenna to Monza (just outside Milan) then direct to Luzern. There is one train at 13:27 but you can't buy it on Trenitalia site. I went to the swiss site for trains http://fahrplan.sbb.ch/bin/query.exe/en and for Varenna to Luzern they have a few routes daily that you can purchase. Most have 2 connections that Roberto mentioned above of Monza to Arth-Goldau

I have no information on trains, but I recommend you stay in the city of Como. We stayed for a week and loved it. It was a 10 minute easy walk to the boat that took us to all the beautiful towns. We drove from Zurich to Lake Como, Genoa, Portofino, Milan, up to Germany, then back to Zurich and home. Even stopped in Nice, France for lunch.

I've also stayed in Como on two occasions and also enjoyed it. The boat service to the lake towns is great and you'll be close to the rail station not having to back track to Milan. And as an added bonus, take the funicular up to Brunante - the views of the lake, city and mountains is spectacular!