The System Lorenz pistol was adopted in 1860, hence it is the Muster 1860 rather than 1859. The pistol shown in your photograph has the safety catch adopted in 1862, hence it is a Muster 1862.
There is no record of any System Augustin or System Lorenz pistols having been imported during the Civil War by either the Federal or Confederate Armies. Since the Muster 1860 pistol had just been adopted and the the Austrian Army was being newly outfitted with them, it is unlikely that any would have been available for export unless they had been rejected by Austrian Army inspectors. The System Augustin pistols were available on the European surplus market, so I can't say that none were imported, just that there is no record of it. Since they were tubelock arms, any imported would have required conversion to percussion by someone prior to export from Europe.
I doubt that many Federal or Confederate troopers would have been wildly enthusiastic about being issued either of the pistols.
Regards,
Don Dixon