Green’s Dictionary of Slang

to use affected manners or speech.

1882		E.V. Page ‘’Arry’ 🎵 It’s ’Arry. ’Arry ev’rywhere, / Doing the La-di-da.
1901		N&Q 6 July 20/2: I like to la-di-da with the ladies .
1901		Bateman & LeBrunn [perf. Marie Lloyd] Folkestone for the Day 🎵 Lord and Lady Thingummy la-di-dah-da-ing round the place.
1901		W.S. Walker In the Blood 116: Slim Jim — was ‘doin’ the lar-dida,’ as he expressed it to himself, in a check suit, soft hat and gloves.
1952		B. MacMahon Children of the Rainbow 203: We went along the corridor, her short steps mincing before me: I saw that she was la-di-dawing me.