To display the mouse cursor position on the map, you first need to find out what the lon-lat coordinates of the map position of the mouse cursor are. In LuciadLightspeed, you can calculate this lon-lat position by first using ILcdGXYViewXYWorldTransformation. It transforms view coordinates to world coordinates. Next, you convert the world point to lon-lat coordinates. You can use TLcdDefaultModelXYWorldTransformation for that.

Program: A component that displays the model coordinates of the mouse cursor (from samples/gxy/common/MouseLocationComponent)
    public ILcdPoint retrieveMouseReadout(ILcdPoint aAWTPoint, ILcdModelReference aReference) throws TLcdOutOfBoundsException {
      TLcdXYPoint worldPoint = new TLcdXYPoint();
      ILcd3DEditablePoint modelPoint = aReference.makeModelPoint().cloneAs3DEditablePoint();

      fView.getGXYViewXYWorldTransformation().viewAWTPoint2worldSFCT(new Point((int) aAWTPoint.getX(), (int) aAWTPoint.getY()), worldPoint);
      TLcdDefaultModelXYWorldTransformation transformation = new TLcdDefaultModelXYWorldTransformation(
      transformation.worldPoint2modelSFCT(worldPoint, modelPoint);
      return modelPoint;