Hi Rick, Do not confuse the Laconia State School with the Belknap County Farm. They are two separate entities, one a county institution and the a state institution.
I transcribed the State School cemetery on Chemung Rd. and posted it on interment.net The county also has a cemetery for those who died there and the bodies not claimed by a family. I transcribed 42 of them, but there are more. Those are listed on findagrave. You have to do a cemetery search for county in NH, Belknap.
I did not find a Fowler in either one