Actually, reading while lying down by itself has no effect on eyesight. This is provided that you do keep a good reading distance and have adequate light. A good reading distance is about 20 to 30cm. Any form of close reading in any type of position can be considered near-work, which should be avoided.
However, reading while lying down is discouraged because gravity pulls your book towards you. That said, it is more likely you will not keep a good reading distance.
To add on, if you are lying down, it is unlikely that you are getting good light because most of our light sources are from the ceiling.
