Is it possible to take a train from Mennagio to points north into Switzerland?
Or do we have to go to Lugano?
You can take a train from A to B anywhere in Europe as long as both A and B have a functional railway station. I think what you may mean is 'can we take a direct (i.e. no change) train?' The answer, throughout Europe, is 'it depends on where A and B are in relation to the rail network.
Menaggio does not have a railway station so the answer to your question is 'no'.
The nearest railway station is in Como, which has four separate stations. A bus runs from Como San Giovanni station to Menaggio.
You can find train times, details and fares from Como (all four stations) by looking at the official Italian railway website in English.
For stations on the way to Lugano, and into Switzerland, an alternative is to take a ferry from Menaggio to the opposite side of the lake where the railway line runs.
Both Lecco and Varenna-Esino have railway stations and both are served by the mid-lake shuttle. Lecco would be preferable as it has a proper ticket office and ticket machines. Varenna does not...just a travel agency which is housed in the station building:
[original VT link]
Mid-lake shuttle timetable here:
By the way, a very useful tool for finding train times and details from A to B almost anywhere in Europe, and certainly in all EU countries, is the official German railway website. It carrries official data from all the other official country railway websites. It won't give you fares for most journeys other than in and from Germany (and a few routes, to Germany as well) but it will give you train times and details, in English:
You can take a bus from Menaggio to Lugano BUT most of the departures on this route either only run on schooldays (and not in school holidays) or only run on Saturdays.
Note also that not all departures go all the way to Lugano.
I've linked the up-to-date bus timetable below. 'Scol' means schooldays only, 'Fer 6' means Saturday only, 'Gior' means every day (including Sundays), 'Fest' means Sundays and public holidays. There are other variations too...see the first page of the timetable:
There are busses only