Wordorigins.org

The origin of this odd term is unknown. It is an Americanism dating to the middle of the 19th century, but beyond that we don’t know much about its origins.

Lollygag, or as it is often spelled lallygag, has had several meanings. The earliest seems to be something of no worth, nonsense, foolery. From a poem about a dead milk cow that appears in the Sparta Democrat (Wisconsin) on 14 September 1859:

22 Kwarts of milck she give,
As true as Eye dew liv,
but now er 12 Kwart bag
Aint wuth a lallygag,
Poor old thyng!