A lullaby was a soothing tune typically sung to soothe an infant or young child and help them to sleep. Lullabies typically featured simple, easy-to-remember lyrics and a gentle melody.
In 2154, Doctor Phlox considered singing a Denobulan lullaby to soothe Captain Jonathan Archer's dog, Porthos, but ultimately decided against it, as his singing had often driven his children to tears in the past. (ENT: "Storm Front")
In 2369, when Lieutenant Worf visited the Romulan prison camp on Carraya IV, he taught the Klingon children of their culture and amongst the things they learned was that a particular song that had been sung to them as a lullaby was in fact a Klingon warrior's song of victory. (TNG: "Birthright, Part II")
Though not specifically described as such in the episode, Star Trek: Voyager writer Lisa Klink referred to the Vulcan tale of enlightenment "Falor's Journey" as a "Vulcan lullaby" when discussing the writing of "Innocence". 
In one scene of the Enterprise episode "Terra Prime", T'Pol was to have sung to her daughter, Elizabeth, a Vulcan lullaby about why children are never late with their sehlat's dinner, though this idea was scrapped. ("Terra Prime" audio commentary, ENT Season 4 DVD special features)