I can try to answer your question as to who made the first side lever doubles. These would all have been pinfires, made when all manner of fastening mechanisms were being invented and produced. While they all do an adequate job of holding down the barrels, there is quite a range to the strength of these mechanisms, and not all are practical.
The best-known of the early side lever actions is probably JD Dougalls Lockfast patent of 1860. Like all inert slide and drop actions, it is a bit slow in the field and takes some getting used to, but it is strong. The first Lockfast had a lever that was lifted, though most had levers that were depressed downward (I have one dating from 1864). Of the side levers tensioned with a spring, J. Needhams action of 1862 would have been amongst the first of that type. It is somewhat awkward in that the lever is hinged near the breech face, and pushing or pulling it downward is not a natural motion (at least not to me). The spring is an improvement, though. I have a John Blissett pinfire with the Needham lever, dating from around 1863-1864. Finally, the S. & J. Law patent of 1865 was a proper snap side lever, but with a very long throw (and it has a bit of a flimsy feel to it). There were a number of variations on these actions, but I havent seen or tried them in my hands. The 'classic' side lever guns, by Stephen Grant and others, and the various side-cocking actions, appeared much later, starting in the very late 1870s and into the 1880s, almost 20 years after the first pinfire side levers.
The gun pictured is a 12-bore dual pinfire-centrefire gun by The Breech Loading Armoury Company (Limited) of London, made before 1868, with the S. & J. Law patent action.
