You will need the services of a professional appraiser
The value of a 12 gauge NR Davis and Son single shot shotgun actually depends on a couple different things. The condition and age of the shotgun would be highly important in determining the value.
By the serial #
0-150 USD depending on exact configuration, age, condition, accessories, etc..
Blue Book of Gun Values
In order to determine the age of Lefever shotgun, the serial number must be known. However, Lefever shotguns were only made and distributed between 1885-1916.
The Browning website has a page enabling you to find your shotgun's age, but you have to know the type of shotgun you own. Go to the page, then click on the type of shotgun it is - there are 15 types - and then reading the page for that gun's serial numbers. Look for the series of serial numbers that includes the one you are interested in: #48162.
1962-1965 90$ poor condition to 175$ very good condition
N R Davis & Sons operated from 1883 to 1917. Value of a fully functioning double is $150-$250.
There are some published serial number lists.
Go to Browning.com, there is a sn function under customer service.
Browning.com has sn data under customer service.
Old catalogs, old gun books.