The M1879 and M1885 Remington-Lee Navy rifles, as well as the M1882 Remington-Lee Army were indeed issued with spare magazines. As noted above, Mills even manufactured a belt specifically for the Lee. The one's I have seen are made with two pouches (for one magazine each) on each side in the front, with 30 loops for individual cartridges in the back for a regulation load of 50 rounds.
The magazines themselves seem to be fairly plentiful. Back when I had several of the rifles I collected a good number of them so that I would have four spares for each rifle. When I started they were going for $25 each, by the time I was finished they were at $65 each, and last I saw they were around $125 each, but still kicking around. Perhaps they were just common on the West Coast though, since most of the Remington-Lee's seem to have been issued to the Naval Militia in California, Oregon and Washington after the adoption of the Winchester-Lee M1895, and I assume were sold as surplus from those stores at some point after 1900.
The system is an excellent one in fact. In my experience the magazine change for a Remington-Lee is FAR quicker and easier than trying it on a Lee-Enfield, even though the design is approximately the same. Since there is no other way to load the magazines other than removing them from the rifle however, it's pretty obvious that it was the preferred method of reloading the rifle. However, when the magazine is removed from the rifle, a spring-loaded shelf pops out from the receiver allowing it to be loaded and fired as a very rapid single-shot, something which the conservative Ordnance officers looked upon with approval.
Per the US adoption of a Lee system, unfortunately in 1892 when the Army put out its request for submissions to the Magazine Rifle Board, Remington (which held the US Patents on the Lee system) was in deep financial straights, and I believe even in receivership, so they didn't manage to submit their proven design to the board. Lee did submit two other designs (one being adopted by the US Navy in 1895), but sadly not the proven M1885. Sad really, since it's a much better design than the Krag, as the Brits have long since proven.
Cheers,
Gordon