Rotate object by clicking on it with animation

Hello there! I searched for days now and can’t seem to find what I am really searching for…
I want to roate an object in Unity 90 degrees, by clicking on it. And I did and it works, the problem is that I want to “show” the movement to the player, and not have the object be 0 degrees on frame 1 and 90 degrees on frame 2. I want the object to gradually rotate to 90 degrees. I want to “animate” the movement, although without using animator on the object.

I used Time.deltaTime and it didn’t rotate gradually(maybe I am using it somewhat wrong?)

Any help would be highly appreciated!

Heres with what I am working with (code)

private void Update()
    {
        if (!completion) //checks weather the picture is completed, if not, it lets you click
        {

            if (Input.GetMouseButtonDown(0)) // checks weather you hit the left mouse click
            {
                RaycastHit hit;
                Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);

                if (Physics.Raycast(ray, out hit, 100.0f)) // checks if it hits the object
                {
                    if (hit.transform != null)
                    {
                        PrintName(hit.transform.gameObject);
                        hit.transform.Rotate(0f, 0f, 90f); // rotates the clicked tile 90 degrees
                        
                        //hit.transform.Rotate(0f, 0f, 90f * (Time.deltaTime * rotateSpeed)); //doesn't show the movement
                    }
                }
            }

You can set a target rotation and lerp to it.

using UnityEngine;

public class RotateOnClick : MonoBehaviour
{
    public Vector3 RotateStep = new Vector3(0, 90, 0);

    public float RotateSpeed = 5f;

    private Quaternion _targetRot = Quaternion.identity;
    
    private void Update()
    {
        transform.rotation = Quaternion.Lerp(transform.rotation, _targetRot, RotateSpeed * Time.deltaTime);
    }

    public void OnMouseDown()
    {
        _targetRot *= Quaternion.Euler(RotateStep);
    }
}