In order to understand this word, we need to take it apart just a little. The "l" at the beginning is a prefix meaning "to." The "-ei" at the end indicates that the word is in "s'mikhut," the grammatical term meaning conjunctive form, that is, it is attached to the word that follows. So "lisheinei" is the elaborated version of "y'sheinim," from the verb "lishon" which means "to sleep." The word means "to those who are sleeping." Whew.
The fact is that nobody knows what sleep really is, but we do know that when we sleep, we are not conscious of the physical world around us (if we are sleeping well). I once had a discussion with a Hebrew teacher who was drilling us in conjugation of verbs. Wanting to be accurate, I asked, "How do you say `I am sleeping' in Hebrew?" She said, "You cannot." I said, "What do you mean? It has to follow some form!" She replied, "You cannot say it because if you are sleeping, you cannot say `I am sleeping!'" I guess you can't argue with that.
Though it may be a little hazardous to suggest sleep to people who are praying in an unfamiliar language, it is important to understand the context of this reference. The phrase that precedes the sleepers refers to God as establishing, fulfilling, sustaining faith with them. And therein is the lesson of the importance of unconsciousness.
In order to relinquish consciousness for a nap or for the night, we have to trust that we will not be betrayed in the interim. You have likely had the experience of losing sleep because your mind wants to resolve a dilemma that defies resolution – you won't give up thinking out of worry. But the world (with the dilemma) is the same upon awakening. The positive context of relinquishing consciousness is this assurance that even when you do not know it, God's faithfulness is constant. As Sovereign of the Universe, God could get away with just about anything if you weren't watching and deny culpability, as if such a thing were possible. But we are assured otherwise.
It may be hard to embrace such an anthropomorphic image of God, but the lesson for us is very down-to-earth. The behavior that this image models is a measure of our own integrity. Do we maintain our faithfulness to the ideals and values we articulate even when no one is conscious of our behavior? To do so is one of the qualities we highlight about God, and we who are in God's image should strive to imitate it.