My understanding is that the USN/USMC bought 15,000 Model 1895 Lee Navy rifles from Winchester in 2 orders, the first for 10,000 and the second for 5,000.  There is some discrepancy in my references, but apparently the bulk of production was completed late in 1897.  The USMC & USN used the rifles & Colt machine guns in the war with Spain, in the Philippines and in China.  The 6mm cartridge was found to be lacking in accuracy at ranges greater than 800 yards and to lack knockdown power.  The relatively thin rifle barrels did not last long with corrosive primers, hot burning propellants and steel jacketed bullets.  The problems were with the cartridge, not the rifle.

In 1900, the USN/USMC adopted the Krag and the 30/40 cartridge, replacing the Lees with Krags whenever & wherever possible, presumably on a unit-by-unit basis.  Within a couple of years, the Lees were gone, mostly sold to Bannerman.  Springfield Armory was working on a Krag replacement beginning in 1900, but the Krag was available in quantity & was still in production. 

With the expansion of forces in WW1, there were not enough 1903s to go around.  Krags remained in service with units that would not see prolonged ground combat in France & that would not need to rely on the AEF in France for ammunition resupply.  Krags would have remained in ships' armories and probably would have been issued to the Fleet Marines in 1917-1918.  The 1903s were needed by the Marines on the ground in France.

The USN/USMC retained Krags as sub-caliber training devices for many years.  In 1961-62, I was a flunky at Lualualei Naval Ammunition Depot & participated in an inventory.  There was Krag ammo (M-1925 180 grain sub-caliber loads) still in the magazines.  I wrote it on my clipboard & asked about it.