Camera Smooth Follow script

So I wrote my own smooth follow script, but I can't seem to get one part of it to work.

I'm making a game with flight mechanics, so when I rotate the ship, I want the camera to follow the rotation. All of this works on the z-axis (up and down) but not on the x-axis.

Here's the script:

 using UnityEngine;
 using System.Collections;
 
 public class Follow : MonoBehaviour {
 
     //Transforms
     public Transform target;
 
     //Floats
     public float speed;
 
     // Use this for initialization
     void Start () {
     
     }
     
     // Update is called once per frame
     void Update () {
         transform.position = Vector3.Lerp(transform.position, target.position, Time.deltaTime * speed);
 
         transform.LookAt(target.parent);
     }
 }