Actually the Syracuse Lefever is a box lock action with side plates and not a true side lock action as might first appear; about the only parts contained on the side plates themselves are the cocking indicators. The Grade G Lefever was one of the most popular model Lefever guns sold; and its price point was on the upper end of the lower Lefever grades spectrum, as Lefever gun grades were produced in ascending order as follows: DS, I, H, G, F, E, D, C, B, A, AA, Optimus, and Thousand Dollar Grade with "Presentation" grades built throughout the entire price range. As to your odd choking, you have one of two likely scenarios. The first is that the gun was built for a left-handed shooter; therefore the first barrel fired would logically be the left tube and would have been ordered with a slightly more open chokes, and the second barrel would therefore be the right tube and be bored with the tightest choke. To determine if the original shooter was right of left handed, check trigger bend; the rear trigger will be bent accordingly.
Another theory about the odd choking combination was related to me at the recent Southern Side x Side by an old pigeon shooter when I discovered that an 1893 vintage 30" 10-bore SAC gun I was inspecting was reverse choked; and the trigger bend definitely indicating the gun to have been set up for a right-handed shooter. I was told that many old time pigeon shooters ordered reverse chokes believing it gave them an edge in competition. The idea was to have the tightest choke in the first barrel so that any pigeon would be completely smashed with a center pattern hit. But, in the event the shooter was slightly off and the bird not knocked down, the second and more open choke increased the shooters odds of a good hit; especially the odds of breaking a wing and dropping the bird inside the pigeon ring so that it was scored as a kill.