In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Grainsby like this:
GRAINSBY, a parish in Louth district, Lincoln; 3 miles WNW of North Thorseby r. station, and 6½ S of Great Grimsby. Post town, North Thorseby, under Louth. Acres, 1, 167. Real property, £1, 965. Pop., 124. Houses, 24. The property is divided among a few. Grainsby Hall, a fine mansion, with greater part of the land, belongs to the Haighs. The living is a rectory in the diocese of Lincoln. Value, £285.* Patron, J. Johnston, Esq. The church is good, and has a tower.
GB Historical GIS / University of Portsmouth, History of Grainsby, in East Lindsey and Lincolnshire | Map and description, A Vision of Britain through Time.
Date accessed: 30th March 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Grainsby ".