Glad you asked about the 6mm Lee Navy / USMC Rifle. I have been starting to collect data on that rifle, but don't have nearly enough yet.
In 1892 the US Army held trials on Governors Island New York for a rifle to replace the single shot 45-70 Springfield Trap Door.
Please note that some other countries had already gone over to bolt action repeating rifles, such as the Norwegians, the Danes (Krag Rifle) and the model 1891 Mauser was already being sold around the world, with the improved model 93 Mauser about ready to hit the market.
In the case of the Army, the contract went to the Krag design which started production around 1894.
While the Army was in a bind to catch up with every one else in the 1890s, the Navy and Marine Corps already had the Remington-Lee 1885 repeating rifle in caliber 45-70..
Before the times of aircraft and fast troop ships, the only way to put a hurtin' on somebody far away was the Navy and Marines.
So the Navy already had experience with Lee designed repeating rifles for almost 10 years. Furthermore, the Navy and Marine rifles were bought on a smaller scale, so the cost of huge contracts became less of an arguement compared to how much damage a few Marines could do when armed with rapid firing repeaters.
The rifle was designed by James Paris Lee and was accepted by the Navy in 1895. Manufactured by Winchester beginning in 1896, with an initial order of ten thousand , around twenty thousand were finally produced.
The 6mm Lee Navy was the first US cartridge to use a metric designator. It was also the smallest diameter round to be used up until the 5.56mm.
The action was a camming action which appears to be a straight pull at first glance. The bolt has to be pulled up and then back. During that time period, Ross of Canada, Steyr of Austria and Schmidt Rubin of Swizterland were all trying to push straight pull or camming actyion rifle designs.
When Winchester developed the 6mm Lee Navy round, it had to buy extra property to extend the test firing range to 1,000 yards.
Another feature that made to Lee Navy more advanced was the fact that it could use Charger (stripper) Clips to rapidly load the magazine. The New Army rifle (the Krag) had a side loading box magazine that did not accept charger clips.
The Army treated to Krag as a single shot rifle, with the fully loaded side magazine being held in reserve. The Krag and later the 1903 Springfield had a magazine cut-off which kept the bolt from going all the way to the rear. thus the rounds in the magazine were not picked up until the switch was changed.
The Marines and Navy had a different point of view. They figured (just like the new Mausers) that the ability to rapidly load the magazine with charger clips meant that the extra cut-off feature was not needed.
They needed to kill lots of folks in a short period of time, in some far off land...
The USMC basic issue ammo belt for the 6mm Lee Navy Rifle was 180 rounds of ammunition in 5 round clips. During the Cuban war the US Army went to troops carrying 100 rounds of 30-40 ammo in looped belts. That was a LOT of ammo for a basic personal issue compared to most other forces on the planet at that time. They also had Colt machine guns in the same 6mm Lee Navy caiber.
The cartridge had more velocity, a flatter trajectory and better penetration against steel plating than the 30-40 Krag round adopted by the Army.
The 6mm Lee was a 112 grain bullet at 2,500fps to 2,600fps depending on the ammo types, while the original 30-40 Krag loads were a 220 grain bullet at 2,000 to 2,100 fps.
The ammuntion was also lighter and allowed the rifleman to carry more rounds.
The rate of fire was fairly fast in the hands of Marines and Navy Landing Party members. During the Cuban action (Spanish American War), one captured Spanish General complained about the American machine gun forced which had forced his surrender. It turned out that there were no machine guns in that area, just US Marines which Lee Rifles.
The Lee Navy did have some problems. It was not as soldier proof as the Krag. The metalurgy at the time was not up to the job and bore errossion was a problem.
Production stopped around 1902 and eventually all the Navy and Marine rifles were replaced with 1903 Springfields.
Sorry for the typos, the wife wants on the computer....