What is the name of this film? I think it might be " A Month By the Lake"

You are correct. The film is indeed called "A Month by the Lake."

"For 16 years Miss Bentley has been spending April at an elegant
hillside villa on Lake Como. This year, 1937, her London society
artist father has recently died and the only other English-speaking
guests are brash Americans. Then Major Wilshaw arrives. He suggests
they meet for cocktails and Miss Bentley stands him up -- not even
thinking about it -- as she helps the new nanny of an Italian family
settle in. Miss Beaumont, a tall, young American who has dropped out
of finishing school in Switzerland, is bored and finds some amusement
in flirting with the major, whose libido is awakened for the first
time since before the great war. And Miss Bentley now finds more about
the major to admire than his ears."

Internet Movie Database
http://imdb.com/title/tt0113849/

The Internet Movie Database, linked above, provides quite a bit of
information about the movie's cast and production crew.

Here you can buy the film on VHS videotape or DVD:

Amazon: A Month by the Lake (VHS)
http://www.amazon.com/gp/product/offer-listing/630401144X//103-3517304-5522259?condition=all

Amazon: A Month by the Lake (DVD) 
http://www.amazon.com/gp/product/offer-listing/B00008L3S3//103-3517304-5522259?condition=all

If you are curious about the beautiful villa where the movie was filmed:

"Just a bit further north up the lake is the incomparable Villa
Balbianello. Arguably, this may just be the most magical home in all
of Italy. Featured in the film 'A Month by the Lake' (in itself a
great travelogue for Lake Como), the villa's loggias, terraces, and
architecture cascade down the slopes of a promontory. Built by the
will of Cardinal Angelo Maria Durini at the end of the 18th century,
this stunning setting is now open to the public by launch access, the
best and usually only way to start your visit."

Voyages International: Lake Como, Italy
http://www.voyagesintl.com/02_custom_archive1.html

This page has some information about the villa, and a very nice photo:

Bassorilievo Italiano: Villa Balbianello
http://www.bassorilievo.it/villabalbianello.htm

Google search strategy:

Google Web Search: "a month by the lake" "lake como"
://www.google.com/search?hl=en&ie=UTF-8&q=%22a+month+by+the+lake%22+%22lake+como

I hope this helps. If anything further is needed, please request
clarification; I'll be glad to offer further assistance before you
rate my answer.

Best regards,
pinkfreud

Great answer, & fast, too!!!! Thanks