Hey P.G.! Thanks for the reply!
We don't--especially in America--hear too much about the Lombard mandolin because of the immense popularity of the Neopolitan model that really came into the spotlight in the early 1900's with travelling European mandolin orchestras. Then of course, Bill Monroe brought the Neopolitan style in deeper into American music. Nowadays, many people recognize the mandolin as a great folk instrument, but aren't aware of its varied history.
The Lombard variant is actually very closely related to the lute (in design, tuning, and playing style--with the fingers, not a plectrum). And it is believed that it was this model for which many of the Baroque composers wrote their mandolin pieces. This of course would make those pieces sound quite different than how we hear them today.
The Neopolitan model--developed around 1740--came about, I believe, as an alternative instrument for the violin (since it's tuned just like the violin) since it was the violin that had become the most highly regarded instrument in both folk and concert settings. In its early years, it gained more acceptance in France and Austria than in its homeland.
Nobody really knows why they are both named mandolin. Fabrizio may be able to confrim this, but it is derived from the Italian word for almond (making it a "little almond," smaller than the mandola/mandolo. Since the Lombard model had been around for a few hundred years more, it is assumed its body looked very similar to an almond. Perhaps the later model was so named because it is also small and high-pitched.
I do not yet own or play a Lombard mandolin, but I'd love to get one and learn it. However, many classical pieces have been transcribed for Neopolitan mandolin--there are even mandolin quartets (2 mandolins, mandola, mandocello) that play string quartet
I think you'll find it lots of fun if you ever decide to take it up! You must tell me about the piccolo; I have no knowledge of it whatsoever. except that it looks dreadfully difficult to play!