We investigate a unique kind of bilayer cylinder structure with loss in core and gain in shell, which exhibits the fascinating properties of switching between coherent perfect absorption and lasing by changing the excitation channels with different angular momentums. In this paper, such cylinder can act as coherent perfect absorber (CPA) under the excitation of monopolar waves, while it becomes a laser under the excitation of dipolar waves. We also show that a CPA can be switched to a laser by covering a metasurface which has ability to change the monopolar wave into dipolar wave. Our work demonstrates a different approach for implementation of transition between CPA and laser.