How to make Smoothfollow align with targets local Z rotation?

So I want the camera to smoothly stay behind an aircraft, meaning it will lerp to its target rotation and position (with distance/height offset) over time.
I know it has been asked like a thousand times, but I always get a camera movement jitter when the physics based jet moves and rotates.
This is the camera-script:

public Transform target;
public float distance = 6f;
public float height = 1.5f;
[Range(0f, 1f)]
public float lerpSpeed = 0.7f;

void LateUpdate(){
 transform.position = Vector3.Lerp(transform.position, target.position + (target.forward * -distance) + (target.up * height), Time.deltaTime * lerpSpeed * 60f);

transform.rotation = Quaternion.Lerp(transform.rotation, target.rotation, Time.deltaTime * lerpSpeed * 60f);

The standard SmoothFollow is not causing any jitter, however it follows the target at global XZ-plane, meaning it does not rotate when target rotates around its local z-axis (transform.LookAt aswell).

How can this be achieved?

Why dont you use transform.lookat instead of rotation ?

I think that even if you dont lerp it, it will look ok because your jet is traveling at high speed so its movements will not be sooo fast…