There's no model number. The model name is Nitro Special, and it was made from 1921 to 1947.
There is a serial number. It appears in 3 places.
Take the gun down by pulling on the foreend from the front. There's a little space for your finger to get under the wood. Pull away from the barrel. The foreend is held on by a spring-loaded latch and it should release with enough pressure.
Look at the metal part that runs down the middle of the foreend. The serial number appears there. Then, remove the barrels. You will find the serial number underneath the left barrel right under the chamber. The third place you will find it is on right side of the receiver, where it meets the right barrel.
This chart will tell you the age of the gun:
http://www.diamondgunsmithing.com/page46/page46.html
It was made by Ithaca. Ithaca bought Lefever in 1916. The Nitro Special was very similar to the NID, and the 16 Gauge version handles very well IMO (I've got one, if you didn't guess that by now
). It's an excellent way to get into a gun that's substantially like the Ithaca NID, which has gotten harder to come by at a reasonable price lately. AFAIK Ithaca tested the design out as a Lefever, before making it as an Ithaca 4 years later.
I use mine in the field occasionally. I had to do a bit of stock repair, due to old oil soaking into the walnut and breaking it down. Unfortunately, my repair didn't end up being a good color match (walnut of different origin
). Sometimes, I toy with the idea of having it all restored. However, it still looks decent and works great. Mine dates to 1926.
My gun has a 2 3/4" chamber. AFAIK all of the Nitro Specials do, which means you can use modern ammo in them (within bounds of reason, of course -- not an issue for the 16 Gauge, since there haven't ever been 16 Gauge super-nitro-turkey-ultra-magnum loads). Check your chamber first, to be sure. I don't want to be responsible for damage or injury; this is, however, the best information I could find when I researched it.
The choke constrictions are marked under the barrels, also. They're numbers, not like modern tick marks or letters. Mine reads 2 on the right, 4 on the left, which is M/F.
Diamond Gunsmithing is one place that will fix the gun up, do any repairs, refinishing, etc. Doug Turnbull is another. These guys make stocks for them:
http://www.classicgunstocks.com/
If you want to see what a restored one looks like, see
http://www.classicgunstocks.com/Nitro_Special_Restoration.html
There's a Lefever forum, although it does lean towards pre-Ithaca Lefever shotguns.
http://lefeverforum.informe.com/lefever-firearms-df3.html