I've been curious about side-levers for quite awhile. Somehow they always made sense and as you know from previous post, just purchased a Reilly Side-Lever SN 27553 (1885).
I went back to look at my Reilly database which has pics of just about every extant Reilly (Reilly made just about every type of action). Here are the two earliest ones:
No SN mentioned, pinefire - has to be mid-1860's:
SN 17392 (Which would date to late 1871-early 1872)(one of Terry Buffum's guns):
The earliest Reilly advertisement which
specifically mentions "side-lever" however is 1877 Bradshaw guide to the Tyrol:
