Smoothly rotate ship in the direction of movement using lerp

Hello all first post ever!

I’ve been working on a project and need a little help understanding lerp.

The idea is for the player to click a location in space and have the ship rotate to that location. I’ve got that part down but now I want the ship to slowly list towards the direction of travel and list back when its nearing the desired rotation.

I’ve poked around the forums and couldn’t find what I was looking for.

Code is as follows:

public class PlayerMovement : MonoBehaviour {

    private Ray moveRay;
    private RaycastHit moveHit;
    Vector3 targetDir;
    Vector3 newDir;
    public float tiltSpeed;
    public float rotationSpeed;
    public float speed = 0;
    public GameObject movementTarget;
    static float t = 0.0f;
	
	// Update is called once per frame
	void Update ()
    {
        //Move the ship forward according to speed
        GetComponent<Rigidbody>().velocity = transform.forward * speed;

        //Let user adjust speed
        if (Input.GetKeyUp(KeyCode.KeypadPlus))
        {
            speed += .25f;
        }

        //Get user input for destination
        if (Input.GetMouseButtonUp(0))
        {
            //Debug.Log("Mouse Clicked");
            moveRay = Camera.main.ScreenPointToRay(Input.mousePosition);
            if(Physics.Raycast(moveRay, out moveHit, 100))
            {
                //Debug.Log("Shooting Ray");
                if (moveHit.collider.CompareTag("NavPlane"))
                {
                    movementTarget.transform.position = moveHit.point;
                    //Debug.Log("Ray Hit Setting Destination");                 
                }
            }
        }

        //Find the target direction
        targetDir = movementTarget.transform.position - transform.position;
        //Create a new rotation with the target direction
        newDir = Vector3.RotateTowards(transform.forward, targetDir, rotationSpeed * Time.deltaTime, 0.0F);
        //Execute rotation
        transform.rotation = Quaternion.LookRotation(newDir);

        //Need help here
        //Find out which direction we are turning
        Vector3 tiltVector = Vector3.Cross(targetDir, transform.forward);
        //Debug.Log("Tilt Vector " + tiltVector.y);

        //if we are turning left rotate to 30
        if (tiltVector.y > 0)
        {           
            transform.Rotate(Vector3.forward, Mathf.Lerp(0, 30, t));
            t += 0.01f;
        }
        //if we are turning right rotate to -30
        else if (tiltVector.y < 0)
        {
            transform.Rotate(Vector3.forward, Mathf.Lerp(0, -30, t));
            t += 0.01f;
        }
    }
}

This is not achieving the desired effect. The ship will slowly list towards the direction of travel but the t vairable gets too high. I’m not sure how to cap it or if it is even possible. I feel like I am not approaching the problem the right way. If lerp isn’t the best option here I am all about learning new techniques. Any help would be appreciated.

Cheers!

You could potentially cap t like this:

t = Math.Min(t + 0.01f, 1.0f);