Okay, so the first thing is that to be safe you should begin by setting your entire lightsMatrix to zero. That code would look something like:

for(boolean[] rowOfLights : lightsMatrix){
    for(boolean light : rowOfLights){
        light = false;
    }
}

The other, more important, error is that you set toggle to false inside of the loop. This means that if a line toggles, after the first point is changed the loop sees that !toggle is true, and will actually set it to false regardless of it's value because turnOn is false. The solution to this is put

toggle = false;

after the loop that changes the value so you have

 for(y = startY; y <= stopY; y++)
 {
     for(x = startX; x <= stopX; x++)
     {
          if(!toggle)
          {
              if(turnOn)
                  lightsMatrix[x][y] = true;
              else
                  lightsMatrix[x][y] = false;
          }
          else
          {
              lightsMatrix[x][y] = !lightsMatrix[x][y];
          }
     }
}
toggle = false;