Lucidity was a state of clear organized thought, as opposed to insanity, hysteria, and delirium.
In 2267, James T. Kirk notified a nurse that if Robert Johnson and Elaine Johnson's lucidity returned, she could find him in the briefing room. (TOS: "The Deadly Years")
In 2372, The Doctor cautioned Kathryn Janeway that a mutating Tom Paris wavered between lucidity and derangement. (VOY: "Threshold")
In 2374, Tim Watters described Captain Ramirez's initial condition as injured, but lucid, refusing to head to the USS Valiant's sickbay. (DS9: "Valiant")