Methods and systems for an electric drive axle of a vehicle are provided. An electric drive axle system includes, in one example a gear train configured to rotationally attach to an electric motor-generator, the gear train includes an output shaft having a clutch arranged thereon and configured to selectively rotationally couple a gear to the output shaft. The gear train further includes a lubrication channel extending between an output shaft and an axle shaft and including an outlet extending through the output shaft and opening into the clutch.