Well, they don't have the same *exact* meaning, but song, melody, or even hymn or carol could be appropriate based on the lullaby. Here is a helpful page from thesaurus.com: http://thesaurus.reference.com/browse/lullaby There isn't actually an entry for lullaby, but that page has some helpful options because it goes over the root word, and some fairly close synonyms.
Renesmee's lullaby
rhyme
Nocturne
Nocturne - APEX
LUCY LULLABY
Usually Brahm's "Lullaby"
Mune Ni Himeta Omoi
Pantoum
Lullaby of the Earth was created in 1970 by Japanese composer Isao Tomita. The piece was inspired by Japanese poet Kenji Miyazawa's poem of the same name.
Bella's lullaby
goodbye lullaby by avril lavigne
The use of end rhyme