The hypothesis was that there should be a difference due to the speed of light being dependent upon the speed of the source relative to the medium (the ether). L1 and L2 were perpendicular to each other so as the earth changed its position relative to the ether, there should be a difference between times taken for light to travel the two paths. As it turned out, there was a null result. No time difference was observed.
But you would not know which direction the ether wind is travelling, so you would not know how either path is oriented to the ether wind. All you are interested in is measuring the magnitude of the time difference.