Historians and Military Experts - Why were repeater rifles/lever-actions not outright adopted by militaries during the First World War and are there any recorded instances of them being used in any major conflicts outside of WW1?

I have been summoned.

Lever actions did see some use in combat in the years leading up to and including WW1, but were limited to either incidental use or secondary roles for infantrymen whenever they popped up. Early use of lever-actions was hamstrung by a reluctance by armies to move adopt repeating rifles for fear of the logistical strain on ammunition, but even once armies got past that issue, lever-actions consistently struggled to hold up to the higher powered ammunition that armies wanted their infantry rifles to be firing.

As far as I'm aware, the first major combat uses of lever-action rifles popped up in the US Civil War. The Spencer and Henry were the two most prevalent lever-action rifles in the war, but they saw fairly limited use. Both were prevalent with cavalrymen, and as far as I'm aware at least one unit in Grant's Overland Campaign had Henry rifles purchased by their commander. Although the firepower of these rifles was greatly appreciated by both the shooter and shoot-ee, they fired cartridges significantly weaker than what infantrymen with standard muzzle-loading rifles were shooting. The Henry was a particularly egregious case of this - firing a large, slow-moving bullet, it lost energy quickly with distance and meant that, even if one could hit a target at ranges beyond a hundred yards, the round was far less likely to incapacitate anyone it hit. So while the Henry and Spencer shined in close-range situations where volume of fire was paramount, they lacked the range and power to be useful out to the ranges armies wanted from an infantry rifle. When the US adopted the Trapdoor Springfield postwar, all repeaters would be phased out, even among cavalrymen.

Outside of the Civil War, lever actions would see incidental use, but continued to struggle from a combination of being incapable of handling the military cartridges of the time and a general reluctance to adopt repeaters. They would make a major showing at the Battle of Plevna during the 1877 Russo-Turkish war, which is often cited as the incident that provided the impetus for the adoption of repeaters. The Turks had significant numbers of Winchesters to complement their single-shot Peabody Martinis. While the Martinis outranged the Winchesters, the Turks were able to leverage the high fire rates of the Winchesters to fend off assaults to great effect during the battle.

Back in the US, lever-actions were considered by the US Army during their fairly regular magazine rifle trials, but they would never be adopted. The 1876 trials saw Winchester submit a modification of their 1876 rifle rechambered to .45-70 (the Army's standard cartridge of the time), but the action wasn't quite strong enough for the power of the cartridge. It wouldn't be until 1886 that Winchester would produce a model that was capable of handling cartridge like .45-70, but that same year it was made obsolete by the appearance of smokeless powder. Smokeless powder is significantly more powerful (and thus produces more stress on the action) than black powder, and that meant that another, more powerful action would have to be developed for lever-actions to be viable with this next generation of military cartridges. Winchester and Savage would put in a decent effort, both submitting lever-action designs to the US smokeless powder rifle trials in the 1890s, but they lost out to the Krag Jorgensen.

Winchester and Savage would continue to refine the designs and pitch them as both civil and military rifles, but they'd only see limited success. Savage's 1895 model's only success as a military platform was to Canada, where it merely served to displace rifles in domestic security roles to free them up for the front. Winchester got luckier with their 1895 model, but only due to the sheer desperation of the Russians for any rifles they could get their hands on.

Russia would order several hundred thousand Winchester 1895s, which Winchester had adapted to take the Russian 7.62x54r cartridge, Mosin-Nagant stripper clips, and a bayonet. Though the order was cut short by the Russian Revolution in 1917, they would serve through the Russian Civil War (with examples popping up regularly in the hands of Latvian troops). Once the Spanish Civil War kicked off in the 1930s, the Soviets would send their non-standard surplus rifles in their inventory off to the Republicans, and these Winchesters were among the rifles sent.