The Residents have a song called “La La” on The Commercial Album. It’s very short (as are all the tracks thereon) and the lyrics are all “la la (etc.)”.
As for Jersey Girl as previously mentioned, Holly Cole has a good version of it on her Temptation CD.
And of course there’s the Teletubbies theme – “Tinky Winky! Dipsy! La La! Po!”
I only vaguely remember the Banana Splits, but I did grow up watching Sesame Street. With all the Muppet fans around here, why is it that I’m the first one to mention Sing? Some versions of Joe South’s Games People Play has “And you don’t give a la duh da duh da.” instead of “And you don’t give a damn.” It appears Dolly recorded a version missing that part of the verse but has additional la-las in the chorus.
Many many lonely nights go by, I sit at home alone and I cry over you. What can I do. Don’t want no one else cause “Baby It’s you” by the Shirelles, also redone by the Beatles.
There’s a lot of Bérurier Noir songs with la la la in them. One example is Vivre libre ou mourir. I must warn you that some of their lyrics can be pretty gruesome. Great music, though!