Light2D works is that it brightens the image. You pick a texture for the Light and wherever that texture overlaps with a sprite, the sprite becomes lighter. That means that you can only light objects which are darker than the Light itself. Your sprite is already white, which is the brightest of colours. Therefore, it does not appear lit. You can play with the modes and the colors and see if anything does the trick for you, but do not expect white to become whiter.
What you can do is choose the Mix mode from the Mode menu and set a colour for your Light. Then you can increase the intensity of the Light which will cause the white sprite to bacome tinted.