The story
"Extra life" sense borrowed from Japanese 1UP(ワンアップ) (wan'appu) and perhaps popularized by Super Mario Bros. (1985); but the term existed earlier in multi-player pinball and other arcade games in the 1960s, where "1Up" and "2Up" were used as flashing notifications to indicate who would play next (or who was "up" next in order). See https://www.inverse.com/gaming/1up-meaning-origin-definition-gaming.
Etymology from Wiktionary, CC BY-SA 4.0.