The phrase predates 1812. It occurs in 'The Critical Review of
Annals of Literature,' Third Series, Volume 24, page 391, 1812.
"The Prince Regent comes in for a blessing, too, but as on of
Serico-Comico-Clerico's nurses, who are so fond of over-feeding
little babies, would say, it is but a lick and a promise." This
would imply that early usage included the sense of 'a taste and
then a promise of more later.'