I am not aware of a Remington sxs with a side lever. Of course that could be lack of knowledge. I would love to see pictures of this gun.

Remington made the Model 1893 #3 which was a single shot. It had a top lever, with a cocking lever on the side.

To my limited knowledge the earliest sxs they produced was the 1873, but it did not have a side lever.
The 1873 was designed by Whitmore. They produced this "lifter" as models 1873, 1875, 1876, 1878 and 1879.

Starting with the Remington Hepburn in 1883 they produced a series of rifles with a side lever.

This is the Model 3, single shot.


1873 Whitmore Lifter. You lifted the top lever.


1883 Remington Hepburn


Yes there were guns made in Belgium with the Remington name on them. This was under contract from Remington.

Pete