iTween Switching Paths

I am making a racing game where players can race and switch between three lanes, side by side. I'm using iTween's PutOnPath and PointOnPath functions to travel down the paths. Every time I switch paths though, my game object instantaneously jumps from its current path onto the next path. Is there anyway to make a smooth animation for the object to travel from its current point on the current path to the next point on the next path?

Here is my code:

public class PlayerScript : MonoBehaviour {

 public Transform[] leftPath;
 public Transform[] midPath;
 public Transform[] rightPath;

 private Transform[] currentPath;

 float percentsPerSecond = 0.1f; //10% of the path moved per second
 float currentPathPercent = 0.0f; //min 0, max 1

 bool onLeft = false;
 bool onRight = false;

 //Start is called at the execution of the game
 void Start ()
 {
     //Initially, the player will start on the middle path
     currentPath = midPath;
 }

 //Update is called once per frame
 void Update () {
     chooseLanes();

     currentPathPercent += percentsPerSecond * Time.deltaTime;
     iTween.PutOnPath(gameObject, currentPath, currentPathPercent);
     this.transform.LookAt(iTween.PointOnPath(currentPath, currentPathPercent+0.001f));

     if (currentPathPercent >= 1)
     {
         currentPathPercent = 0;
     }
 }
 void LateUpdate()
 {

 }
 //Draws iTween path in Scene Editor
 void OnDrawGizmos()
 {
     //Visual. Not used in movement
     iTween.DrawPath(midPath);
     iTween.DrawPath(leftPath);
     iTween.DrawPath(rightPath);
 }

 //Moves the car according to which button the player presses
 void chooseLanes()
 {
     //If the player turns left, they'll enter the path to the left of them
     if (Input.GetKeyDown(KeyCode.LeftArrow))
     {
         //The left path is to the left of the middle path
         if (currentPath == midPath)
         {
             currentPath = leftPath;
             
         }
         //Nothing is to the left of the left path
         else if (currentPath == leftPath)
         {

         }
         //The middle path is to the left of the right path
         else if (currentPath == rightPath)
         {
             currentPath = midPath;
         }
         else
         {
             Debug.Log("Current Path is Null");
         }
     }
     //If the player turns right, they'll enter the path to the right of them
     if (Input.GetKeyDown(KeyCode.RightArrow))
     {
         //The right path is to the right of the middle path
         if (currentPath == midPath)
         {
             currentPath = rightPath;
         }
         //The middle path is to the right of the left path
         else if (currentPath == leftPath)
         {
             currentPath = midPath;
         }
         //Nothing is to the right of the right path
         else if (currentPath == rightPath)
         {

         }
         else
         {
             Debug.Log("Current Path is Null");
         }
     }
 }

}