Etymology for the phrase, "on a lark."

Solution 1:

Both Wiktionary and Etymonline say that the origin of lark in the meaning "frolic, prank" is not clear. Wiktionary puts it like this:

Origin uncertain, either

• from (notably northern) English dialect lake/laik (“to play”) (c.1300, from Old Norse leika (“to play (as opposed to work)”)), with intrusive -r- common in southern British dialect; or
• shortening of skylark (1809), sailors' slang, "play roughly in the rigging of a ship", because the common European larks were proverbial for high-flying; Dutch has a similar idea in speelvogel (“playbird, a person of markedly playful nature”).

Solution 2:

The OED's earliest citation is for the noun lark, in in Lexicon Balatronicum: a dictionary of buckish slang, university wit, and pickpocket eloquence (1811):

Lark, a piece of merriment. People playing together jocosely.

Their etymology is:

Possibly it may represent the northern lake v.1 [To exert oneself, move quickly, leap, spring; hence, to fight. Obs.], as heard by sporting men from Yorkshire jockeys or grooms; the sound /læək/ , which is written lairk in Robinson's Whitby Glossary and in dialect books, would to a southern hearer more naturally suggest ‘lark’ than ‘lake’ as its equivalent in educated pronunciation. On the other hand, it is quite as likely that the word may have originated in some allusion to lark n.1 [the bird]; compare the similar use of skylark vb., which is found a few years earlier (1809).