Actually, the game already gives a quick description of what it does:
Dickon: "There's one that's called 'Deep Sleep.' It's supposed to be a sleeping aid to help people with insomnia."
Belle: "It makes them sleep deeper? Makes it harder to wake them up?"
In other words, Deep Sleep isn't a spell that makes people fall asleep. It only makes you sleep better and deeper. Like most magic in LLtP, these spells aren't something you would find in Dungeons & Dragons. It's not combat magic, and in most cases, the setting's magic isn't even hostile or forceful.
Honestly, I find most magic systems in fantasy settings to be dumb as hell. One of the things I always try to do when building a setting is to have things make sense. I try to imagine what kinds of spells an actual human being might design if he were given the opportunity to subtly affect things or minds around him. Deep Sleep is an example of a spell that isn't really designed to use on others against their will. To the (unnamed) person who designed the spell, that wouldn't even have made sense. Instead, this spell was made to solve the eternal human problem of not getting quality sleep every night, a particularly big problem for bookworms who like to stay up all night poring over their books. Casting Deep Sleep might not make you fall asleep, but it means that when you do, you'll most likely stay asleep for a full night.
Dickon is going to be able to discover a slightly more naughty use for this spell, obviously.