Out of all our sensory organs, we need to stop taking signals explicitly only from eyes in order to sleep. Even interestingly, those who are not able to receive signals from eyes (i.e., the visually challenged people) also need to close their eyes in order to sleep. I wonder what is the relation of closing eyes with sleeping. I think the reason might be related to the state of the muscles related to the eyes. Of course, even if it were the case that one could keep her eyes open while sleeping, the brain would stop paying attention to the signals received by the eyes -- just like the brain stops paying much attention to the signals received by the nose or the ears while sleeping even if these organs are not physically closed or prevented from receiving signals. But in the case of the eyes, they are physically closed while sleeping, which makes me curious.
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 & Sons. p. 215. ISBN 978-0-471-73383-6.