House was called up to help Cleveland's overworked bullpen, which pitched 7 2-3 innings in Friday's 11-1 loss to Oakland. Zach McAllister, who struck out the side in the first, retired only one of the nine batters he faced in the Athletics' eight-run second inning.
Indians manager Terry Francona used four relievers to finish the game after going to the bullpen six times in Thursday's 4-2 loss to Toronto.
House was 1-2 with a 2.40 ERA in seven starts at Columbus. He spent three days with the Indians last season, but didn't appear in a game.
Lee had no record and a 4.76 ERA in 13 relief appearances.