What kind of American walnut?
I'd assume that American Walnut is any species or cultivar of walnut grown in America.
As Miller stated, most Lefevers were stocked in English Walnut, but it is said that some that were assembled by Ithaca after they bought the Lefever name in 1916 were built with stocks made of Black Walnut. I seem to recall than at least some L.C. Smith guns were built with French Walnut blanks. And of course, French Walnut is just English Walnut (Juglans Regia) that was grown in France. Most Fox and Ithaca guns appear to be Black Walnut, but I don't know where those makers sourced their wood.
There are several species of walnut trees grown in America including some hybrids. English Walnut is considered the very best species for gunstocks because of various characteristics including strength, density, ease of machining or carving, and ability to take fine checkering. But those characteristics can also depend upon things like the soil and climate where the tree was grown, how it was cut, dried, seasoned, etc. I have no personal experience with bending walnut stocks, so I couldn't comment on which species is most amenable to taking a bend without either breaking or rebounding.