This item is identified in America's Munitions 1917-18 as a Carrying Case for the Browning Automatic Rifle M1918. Your example manufactured by R. H. Long, Framingham, Mass., in November 1918. Other known contractors were Belber Trunk & Bag Co., Philadelphia, Pa., and Westboro Trunk & Bag Co., Westboro, Mass. It is believed that all were manufactured in 1918. In the contract listings I have researched they are listed as Carrying Case, without any model or purpose. I have speculated that the Army wanted to conceal the BARs to keep them classified until deployed in combat, but I have no such confirmation.
Although intended for the BAR these carrying cases were useful for any long arm, and I have seen one offered for sale in an online auction that had an Ordnance Department part number marked on it that suggested it was stocked during WWII. Yours is the only example I have seen with the leather sleeve or whatever it is, added and I suspect it was probably added by someone that acquired it after it was disposed of by the Army.