A donor to the National Rifle Association filed a lawsuit against the gun-rights group, seeking class-action status, and claiming the group’s funding solicitations were “intentionally and materially false” because the NRA spent donated funds on executive perks, large legal fees, and other expenses unrelated to the group’s core mission.

In the suit, filed in U.S. District Court in Nashville, Tenn., plaintiff David Dell’Aquila is seeking damages on behalf of all donors since Jan. 1, 2015, to the NRA and its related charity,...