Yes there is a Cutlip Road and yes it is in Lick Township. In southern Ohio.
As far as I can tell, there is only one Lick Township in the country, but not so when it comes to Licking. There are in fact TWO Licking townships in Ohio alone, one in Muskingum County and the other in, you guessed it, Licking County.
And there are also Licking townships in Indiana, Illinois and Pennsylvania. The township office for the latter is in Sligo, PA, on Canoe Ripple Road, by the way.
And just where did all this licking come from you might ask. Historically they were places with mineral deposits, usually salts, that attracted animals, much as a salt block does in modern times. Hence all that licking.
Which brings me to French Lick, Indiana. I passed through there on a recent road trip and saw nothing French about it, but when it was founded as a community it was a French trading post near a spring and a natural salt lick.
It was way later in its history that it became known as the birthplace of basketball player Larry Bird, “The Hick from French Lick.”