I have waterfasted several times (for about a week each time) and experienced that while eating light, the sleep is much better. Much deeper and healing deep sleep, much more vivid dreams and much more lucidity.
Doesn't have to be waterfasting of course. Just not eating too heavy at night for several hours before sleep already helps.
Yes, going to sleep slightly 'hungry' indeed increases your chance to have a LD and also improves your sleep.
Investigate "daylight diet" if you're interested in the relationship of diet and sleep.