Why do we need to close eyes to sleep?
Unlike our underwater ancestors, land animals have evolved eye lids or nictitating membranes to protect our eyes and keep them moist periodically by blinking. During the sleep state, closing our lids protects the eyes from drying out and getting damaged while unconscious.  In addition to the lids themselves blocking light stimulus (not totally), our eyes also roll back to attenuate light stimulation.  Fish also sleep and don't need eyelids to do so, thus closing eyes is not a prerequisite for the sleep state.

Textbook Source: Butler, Ann B.; Hodos, William (2 September 2005). Comparative Vertebrate Neuroanatomy: Evolution and Adaptation. John Wiley &amp; Sons. p. 215. ISBN 978-0-471-73383-6.