Original meaning usage and meaning of "la-di-da"

It’s not clear why I should compare it to the older ‘lardy-dardy’. Could anyone clarify? la-di-da | Etymology of la-di-da by etymonline
and what is not addressed is the possible relevance of its being onomatopoeic.

The easiest and more common way to “fake” the French accent: stressing the last syllable. In French, always stress the last syllable

If it is onomatopoeic, what (or who) makes the sound “la di da”?

Lardy dardy defined: Notes and Queries - Google Books

The 1870s la-di-da: All the Year Round - Google Books