Up to 1858 wills were proved in church courts. If the will was proved locally in a Lincolnshire church court then it will be held at Lincolnshire Record Office (and will be indexed so you can just inquire whether they hold the will - bearing in mind not all wills were probated immediately after death).
http://www.lincolnshire.gov.uk/archives/If the deceased owned property across more than one church dioceses i.e. outside the jurisdiction of just a Lincolnshire church court then the will would have to be proved in a higher church court.
For Lincolnshire this could either be the Prerogative Court of York - wills held at the Borthwick Institute.
http://www.york.ac.uk/inst/bihr/Not all wills are indexed.
Or the highest church court of all the Prerogative Court of Canterbury (will index online but not administrations) held by The National Archives.
http://www.nationalarchives.gov.uk/documentsonline/After 1857 wills were probated by the state and the system was centralised.
Regards
Valda
