Unity3D: Overlaying Line Renderer on reflecting Raycast

So I have the Reflecting Raycast up and running. Which is displayed here:

Here is the Code:

 public int maxReflectionCount = 5;
public float maxStepDistance = 200f;


void Start()
{

}


void Update()
{

    Laser();
}


void Laser()
{
    DrawReflectionPattern(this.transform.position + this.transform.forward * 0.75f, this.transform.forward, maxReflectionCount);
}


private void DrawReflectionPattern(Vector3 position, Vector3 direction, int reflectionsRemaining)
{
    if (reflectionsRemaining == 0)
    {
        return;
    }

    Vector3 startingPosition = position;

    Ray ray = new Ray(position, direction);
    RaycastHit hit;
    if (Physics.Raycast(ray, out hit, maxStepDistance))
    {
        direction = Vector3.Reflect(direction, hit.normal);
        position = hit.point;
    }
    else
    {
        position += direction * maxStepDistance;
    }

    Debug.DrawLine(startingPosition, position, Color.white);

    DrawReflectionPattern(position, direction, reflectionsRemaining - 1);


}

What I would like help doing is overlaying a LineRenderer on top of this reflecting Raycast. I have looked up a few things online and watched some tutorials but still cant seem to get it working. Any help would be greatly appreciated!