The lock-up of the gun that is posted has been known to me as the "Jones rotary" or "screw grip" but I see what you mean. Americans are very specific in what is meant by a "lever action"...the Winchester lever action repeater, Stevens single shots such as the 44 1/2 are considered a lever action, as is the Ruger No.1.
Greener called that type (pictured above) the double grip, but I don't trust anything in his book "The Gun" and it's development...but again, I now see how the rotary underlever is just a variation of the Lefaucheux (correct spelling), ...I'll have to re-check and see what Geoffrey Boothroyd has to say on the subject...
Thanks for pointing out the similarities to me, I had not realized that the Jones lever and the Lefaucheux system were exactly the same except one has the English key, and the other the French key...Bob Chambers
