Methot broke his jaw Thursday night in a home loss to Dallas. Lebda broke a thumb Feb. 3 in an overtime win at Anaheim.
Prout was called up from Springfield of the AHL, and York from Chicago of the ECHL. York will fill in for Curtis Sanford, day-to-day with an upper-body injury.
Prout has three goals and four assists in 41 games for Springfield this season. York is 0-1-0 with a 3.53 goals-against average and .878 save percentage in four games with the Blue Jackets this season.