Question about rotating an object thats moving.

You could set a target angle with your input, and then use Mathf.MoveTowardsAngle or similar functions.

Something like this (psuedo code)

 if (left)
    target = -45;
 if (right)
    target = 45;
 
 angle = Mathf.MoveTowardsAngle(angle, target, speed * Time.deltaTime);

Here's an example using Mathf.SmoothDampAngle to give a smooth Z axis rotation. You can setup a bunch of different parameters and press A/D keys (it uses horizontal axis by default). You can also override the tilt with a script of your choice. Just set .tilt to a value between -1 and 1. 0 is forward. The script will overwrite rotation so if you have any other script that is setting rotation you have to modify the code or make either of the scripts a child of the other.

 using UnityEngine;
 
 public class Rotate2D : MonoBehaviour
 {
     // Max tilt angle
     [Range(0, 360)]
     public float tiltAngle = 45;
 
     // Degrees per second
     [Range(0, 720)]
     public float speed = 360f;
 
     // Smaller values is snappier
     [Range(0.01f, 1)]
     public float smoothTime = 0.1f;
 
     // For the lazy, some kind of def. impl.
     public bool useHorizontalAxis = true;
 
     // Provided by script if not useHorizontalAxis
     [Range(-1, 1)]
     public float tilt;
 
     // The current rotation in angles around Z axis
     [HideInInspector]
     public float angle;
 
     // The current angular velocity
     [HideInInspector]
     public float velocity;
 
     void Update()
     {
         DefaultTiltBehaviour();
         UpdateLocalRotation();
     }
 
     void DefaultTiltBehaviour()
     {
         if (useHorizontalAxis)
             tilt = -Input.GetAxisRaw("Horizontal");
     }
 
     void UpdateLocalRotation()
     {
         float target = tiltAngle * Mathf.Clamp(tilt, -1, 1);
         angle = Mathf.SmoothDampAngle(angle, target, 
                                   ref velocity, smoothTime, speed, Time.deltaTime);
         transform.localRotation = Quaternion.Euler(0, 0, angle);
     }
 }