Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
GROWER
As described in historical dictionaries
Patronymica Britannica (1860)
GROWER. In the H.R. Le Grower. Among the religious puerilities of the middle ages was the office of " King's Cockcrower." I have seen in some old wardrobe accounts of (I think) the time of Edward I. entries for the payment of a person for crowing like a cock at the door of the king's bedchamlier at Easter. Hence probably the surname.