His biographer says that Allen & Unwin (his publishers) asked for "a new Hobbit book". The earliest drafts are about a second adventure for Bilbo -- he had run out of money and needed a new treasure fetch-quest.

You can read the early drafts in book 6 of the History of Middle-earth, and watch as "the tale grew in the telling". They start with Bilbo, then the protagonist changes name and identity as the concept fills out. He made it as far as Bree in a very Hobbit-esque style before scrapping it all and rewriting it in the more adult LotR style.

(He later tried to re-write The Hobbit in that LotR style, but it was dreadfully boring and he gave up after a few chapters.)