According to Daniel Cassidy in his insane book, How The Irish Invented Slang, the word lick, as in to beat someone soundly, comes from the Irish word leag, (pronounced lyagg) meaning to knock down, to lower (of a sail) or to lay. The word leag doesn’t sound much like lick and there is no evidence for an Irish origin.
The truth is actually far more interesting, as well as having the great advantage of being true. Lick comes from an earlier expression ‘to lick into shape’ and this comes from the fascinating Medieval tradition of the bestiaries, where moral and religious lessons were read into stories about natural history. A tradition about bears held that the bear cub was formless at birth and had to be fashioned into a correct bear shape by licking. Thus, licking a child into shape came to mean fashioning a child in a moral sense by punishing them and from this came the meaning of giving someone a sound thrashing. In French, people sometimes refer to a badly-behaved child as an ours mal léché, a badly-licked bear!
Cassidy, the Joseph Goebbels of Irish Studies, chose to act like the badly-licked bear that he was and ignore the well-attested and obvious derivation of this word in favour of his own crazy theory.