Lerping from one position to another in a specific amount of time, no matter the distance

I'm playing around with a top down thingy where I want my character to control in a very specific way. The idea is that once I indicate a direction, the character starts moving in that direction until it hits a wall.

My approach is: Have it shoot out a ray and note the hit point where it collides with an object that I've tagged as "wall".

Once it hits a wall, it starts lerping towards that hit point.

My problem is, I seem to be missing something about how lerping works and I can't seem to wrap my head around the logic. It will only lerp part of the way instead of lerping smoothly all the way.

Here's my code:

 public class PlayerController : MonoBehaviour {
 
     public float speed = 30f;
     public float rotateSpeed = 15f;
 
     //Creating an enum to store my directional constants. I really need to learn about enums because I don't know what I'm doing exactly.
     enum Direction{North, NorthEast, East, SouthEast, South, SouthWest, West, NorthWest};
     private Direction playerDir;
     private string direction; //A number based on hDirection and vDirection to let me set rotation to a single number
     private Vector3 fromPosition;
     private Vector3 targetPosition;
     private bool moving;
     private float moveCool;
     private float nextMove;
     RaycastHit hit; //Okay, so I create a Ray called "hit"
 
     void Start ()
     {
         playerDir = Direction.North;
         moving = false;
         moveCool = 0.5f;
     }
 
     void FixedUpdate () 
     {
         float moveHorizontal = Input.GetAxisRaw ("Horizontal");
         float moveVertical = Input.GetAxisRaw ("Vertical");
 
         //Detect input and start rotating the player if there is movement input
         if (moving == false)
         {
             if (moveHorizontal == 0 && moveVertical == 1)
             {
                 playerDir = Direction.North;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == 1 && moveVertical == 1)
             {
                 playerDir = Direction.NorthEast;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == 1 && moveVertical == 0)
             {
                 playerDir = Direction.East;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == 1 && moveVertical == -1)
             {
                 playerDir = Direction.SouthEast;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == 0 && moveVertical == -1)
             {
                 playerDir = Direction.South;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == -1 && moveVertical == -1)
             {
                 playerDir = Direction.SouthWest;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == -1 && moveVertical == 0)
             {
                 playerDir = Direction.West;
                 moving = true;
                 Rotation (playerDir);
             }
             else if (moveHorizontal == -1 && moveVertical == 1)
             {
                 playerDir = Direction.NorthWest;
                 moving = true;
                 Rotation (playerDir);
             }
         }
 
         if (moving == true)
         {
             if (Time.time > nextMove)
             {
                 moving = false;
                 Debug.Log (moving);
             }
         }
     }
 
     void Movement ()
     {
         nextMove = Time.time + moveCool;
 
         nextMove = Time.time + moveCool;
         //I shoot the ray forward (this will always be after I have rotated, so that's fine) and let it continue until it hits something. 
         //Maybe read up on "out hit" at some point. You don't know what you did there.
         if (Physics.Raycast(transform.position, transform.forward, out hit))
         {
             //okay so when it hits something, it's gonna set the update fromPosition with the player's current position and then use the impact point from the ray
             //as the value in targetPosition. So far so good. 
             print (hit.point);
             fromPosition = transform.position;
             targetPosition = hit.point;
         }
 
         transform.position = Vector3.Lerp (fromPosition,targetPosition,Time.deltaTime * speed);
     }
     
 
     void Rotation (Direction playerDir)
     {
         //switch statement - checks against multiple cases of a single variable (playerDir in this case) and takes actions based on different values of the variable. 
         switch((Direction)playerDir)
         {
         case Direction.North:
             transform.eulerAngles = new Vector3(0f,0f,0f);
             Debug.Log (playerDir);
             Movement(); 
             break;
         case Direction.NorthEast:
             transform.eulerAngles = new Vector3(0f,45f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.East:
             transform.eulerAngles = new Vector3(0f,90f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.SouthEast:
             transform.eulerAngles = new Vector3(0f,135f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.South:
             transform.eulerAngles = new Vector3(0f,180f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.SouthWest:
             transform.eulerAngles = new Vector3(0f,225f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.West:
             transform.eulerAngles = new Vector3(0f,270f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         case Direction.NorthWest:
             transform.eulerAngles = new Vector3(0f,315f,0f);
             Debug.Log (playerDir);
             Movement();
             break;
         }
     }

Also, I am very much a newbie at this, so feel free to also point out any redundancies or sub optimal practices. :) Thanks