Kα X-rays are emitted due to the transition of an electron from the L shell to the K shell and Lα X-rays due to the transition of an electron from the M shell to the L shell. If Kα X-rays are not emitted, then the L shell will not be vacant to take the electron from the M shell. Hence, Lα X-rays will not be emitted. Therefore, it is not possible that in a Coolidge tube, characteristic Lα X-rays are emitted but not Kα X-rays.