I have seen conflicting information about luggage storage in Varenna, so I emailed the business that one source stated did provide the service to confirm. I am copying and pasting the response. Hope it helps others with their planning.
"Good morning from "I Viaggi del Tivano",
yes we have luggage storage service; the price is 5,00 Euro each bag for the day.
Our office hours are:
monday to sunday
09.00 am - 01.00 pm // 2.30 pm - 06.30 pm
We are located in the train station building.
If you need more information do not hesitate to contact us
I hope I've been helpful"