Space ship pitch camera help

Hello,

I am working on a camera, which is set to follow the players space ship. I want to camera to have the same rotation as the ships X axis, but I want it's rotation along the Z axis to have a delay. This is what I have so far, but I can't figure out how to make the Lerp happen only on the Z axis.

Vector3 velocity = Vector3.zero;
Vector3 forward = playerShip.transform.forward*-cameraOffset.z;
Vector3 up = playerShip.transform.up*cameraOffset.y;
Vector3 needPos = (playerShip.transform.position + forward) + up;
Quaternion needRot = playerShip.transform.rotation;

transform.position = needPos;
transform.rotation = Quaternion.Lerp(transform.rotation,needRot,4f * Time.deltaTime);