Yes, elves in LOTR do sleep, although it is different from the way humans sleep. Elves are immortal, and their bodies don't require sleep in the same way that humans do. However, they still need to rest their minds and recuperate from the stresses of life, so they do sleep, but in a different way. Elves sleep in a state of deep meditation, which allows them to enter a state of relaxation and reflection. They also use this time to connect with their inner selves and the natural world around them.