Did an online search for you and came up with the following. It appears this place was known by a variety of names over the years.
Kentucky House of Reform, later known as Kentucky Village, later Dr. Luke P. Blackburn Correctional Complex.Wasn't sure about this last one, until I ran across an item on a woman who used to teach there: ""She worked for many years at Kentucky Village (formerly Greendale Reformatory; currently called Blackburn"
Articles pertaining to Gov. Nunn show that during his term one of the items he addressed was: "_Closure of Kentucky Village, an institution outside Lexington where the state for 74 years had committed its juvenile delinquents. Nunn paid a surprise visit to the institution early in his term and was appalled by conditions there. The state switched to a system of regional centers geared to specific age groups, interests and seriousness of offenses. (he was elected 1967)"
So who would have those Records?I think I would contact the Governor's Office, or State Archives if they have one, and go from there....