Tilt an object when rotating and set it back to normal afterwards

Hi everyone,

Here is my problem. I have an object (basically, a moto) and so far I just make it go on a plane. I can make it rotate so it goes left or right whenever I want. Now, as motos do when they turn, I want my moto to tilt when turning. Here is my Movements and ControllerManager class so you can see what i'm working with.

 public class ControllerManager : MonoBehaviour
 {
     public KeyCode forwardKey, leftKey, rightKey;
     public float tilt;
     private float _fwd, _lateralDirection, _right, _left;
     public float Fwd{   
         get { return _fwd;}
     }
     public float LateralDirection{
         get { return _lateralDirection; }
     }
 
     public void Start(){
         _fwd = 0;
         _right = 0;
         _left = 0;
     }
 
     public void FixedUpdate(){
         // _fwd and _lateralDirection kind of simulates default horizontal and vertical axis values
         _fwd += Input.GetKey(forwardKey) ? (_fwd < 1 ? 0.1f : 0) : (_fwd > 0 ? (_fwd < 0.01f ? -_fwd : -0.1f) : 0);
         
         // moto can't turn if not moving forward
         _right += Input.GetKey(rightKey) & _fwd != 0 ? (_right < 1 ? 0.1f : 0) : (_right > 0 ? (_right < 0.1f ? -_right : -0.1f) : -_right);
 
         _left += Input.GetKey(leftKey) & _fwd != 0  ? (_left > -1 ? -0.1f : 0) : (_left < 0 ? (_left > 0.1f ? -_left : 0.1f) : -_left);
 
         _lateralDirection = _left + _right;
     }
 }

 public class Movements : MonoBehaviour
 {
     public float speed;
     public float sensibility;
     private ControllerManager _controller;
     // Start is called before the first frame update
     void Start()
     {
         _controller = GetComponent<ControllerManager>();
     }
 
     // Update is called once per frame
     void LateUpdate()
     {
         transform.Translate(Vector3.right * _controller.Fwd * speed * Time.deltaTime, Space.Self);
         transform.Rotate(Vector3.up * _controller.LateralDirection * sensibility * Time.deltaTime, Space.World);
     }
 }

Any ideas ? I have tried to use Animations but I can't seem to make it work : I created two animations TiltRight and TiltLeft. Each of them simply rotates the moto (~ 25 degrees) around fwd axis, respectively right and left. But I'd need to sort of pause the state of the object while turning key are pressed. And I did not achieve that.

Regards.