Line renderer spring shape

Not sure if you need 2D or 3D solution, so I just made the most universal one that applies to 3D space and can probably be somewhat used in 2D too.

There are a lot of ways to go about it (the beauty of algebra), I created a plane with normal pointing towards second object (from first one) and then created points on that plane moving it along the normal axis:

 public Transform object1;
     public Transform object2;
     private LineRenderer lineRenderer;
     const int NUMBER_OF_POINTS = 100;
     const int NUMBER_OF_REVOLUTIONS = 5;
     const float SPIRAL_WIDTH = 2.0f;
     private void Awake() {
         lineRenderer = GetComponent<LineRenderer>();
         lineRenderer.positionCount = NUMBER_OF_POINTS;
     }
     private void Start() {
         CreateCurveShape();
     }
     private void CreateCurveShape() {
         float objectDistance = Vector3.Distance(object1.position, object2.position);
         Vector3[] points = new Vector3[NUMBER_OF_POINTS];
         for (int i = 0; i < NUMBER_OF_POINTS; i++) {
             // Define plane with normal pointing to second object
             Vector3 planeForwardDirection = (object2.position - object1.position);
             Vector3 planeRightDirection = Quaternion.Euler(90.0f, 0.0f, 0.0f) * planeForwardDirection;
             Vector3 planeUpDirection = Vector3.Cross(planeForwardDirection, planeRightDirection);
 
             // Some additional debug to visualize our plane
             Debug.DrawLine(object1.position, planeForwardDirection, Color.red, 1000);
             Debug.DrawLine(object1.position, planeUpDirection, Color.cyan, 1000);
             Debug.DrawLine(object1.position, planeRightDirection, Color.green, 1000);
 
             // Distance along the object to object axis
             float currentDistanceNormalized = (float)i / (float)NUMBER_OF_POINTS;
             float currentDistance = currentDistanceNormalized * objectDistance;
 
             // New coords on our plane facing the second object
             Vector3 spiralCoords = SPIRAL_WIDTH * planeUpDirection.normalized * Mathf.Sin(NUMBER_OF_REVOLUTIONS * currentDistanceNormalized * 2 *Mathf.PI) +
                                    SPIRAL_WIDTH * planeRightDirection.normalized * (Mathf.Cos(NUMBER_OF_REVOLUTIONS * currentDistanceNormalized * 2 *Mathf.PI) - 1.0f) +
                                    planeForwardDirection.normalized * currentDistance;
             points[i] = spiralCoords;
         }
         lineRenderer.SetPositions(points);
     }

It should work fine no matter how you position your objects in 3D space, maybe some minor modifications might be needed for your specific application. I also threw in number of revolutions and width variables.

Of course the debug lines can be removed. The -1.0f Mathf.Cos moves the starting/ending point to the object (cosine of 0 is 1, so we need to offset it to match our object's position).