There are several possibilities.
1. Add an additional contructor
    public LFrame(String title) {
        this(); // calls other constructor that initializes frame
        setTitle(title);
    }
Then, from x
   new LFrame("x").setVisible(true);
And from y
   new LFrame("y").setVisible(true);

2. Call setTitle() after creating two different instances:
From x:
    LFrame yourFrameFromX = new LFrame();
    yourFrameFromX.setTitle("x");
    yourFrameFromX.setVisible(true);
And from y:
    LFrame yourFrameFromY = new LFrame();
    yourFrameFromY.setTitle("y");
    yourFrameFromY.setVisible(true);

3. Have only one LFrame instance and call setTitle() before setting
frame visible:
    LFrame yourFrame = new LFrame();
Then from x:
    yourFrame.setTitle("x");
    yourFrame.setVisible(true);
And from y:
    yourFrame.setTitle("y");
    yourFrame.setVisible(true);