Douglas Harper's Etymology Dictionary
nonsense refrain in songs, probably from Old English la, a common exclamation; but la-la is imitative of babbling speech in many languages (compare Greek lalage "babble, prattle," Sanskrit lalalla "imitation of stammering" Latin lallare "to sing to sleep, lull," German lallen "to stammer," Lithuanian laluoti "to stammer").
Wikipedia
La-La is a social network / music messaging application for iOS that uses audio instead of written words. Users communicate by sending each other audible song snippets which include music lyrics to conduct their conversations.
"La-La Means I Love You" is a R&B/ Soul song by American vocal group The Delfonics. Released on January 26, 1968 by Philly Groove Records, The song was written by Thom Bell and William Hart and produced by Bell and Stan Watson.
Usage examples of "la-la".
I only mention it because for a moment or two there it sounded like someone else was singing the la-las and dum-dee-dums along with him, kind of harmonizing.
But murder wasn't supposed to happen in a place like La-La Land, not where happy tourists gathered for vacations of a lifetime, where residents pursued dreams that came true every single day, where delightful amounts of money changed hands and everybody had fun in the process.
As confused as he sometimes felt, the other up-time residents were goggle-eyed with shock to find La-La Land's most notorious confidence artist walking the straight and narrow, working the first honest job of his life.
The Land of Nod's borders remained closed, due to breaking off diplomatic relations with the neighbouring republic of La-la Land.
Terribly sorry, your highness, but Sonny Jim has flitted off to La-la Land.