The authority will carry out a consultation on the proposed changes which would save the council £750,000 a year.
The plans would see The Collection expanded to create exhibition space while also taking in artwork from other sites.
While large spaces in the Usher Galley could become a wedding venues or a base for local registration and celebration services.
The Collection could become a major museum.
The council is also proposing to change some of the current office space at Lincoln Castle to open more exhibition areas and learning rooms.
Meanwhile, outside of Lincoln, Gainsborough Old Hall could be returned to English Heritage in October 2020 at the end of its current lease.
The authority is also looking to hand over control of Discover Stamford, Burgh Le Marsh Windmill, Ellis Mill and Alford Windmill.
Moves to change heritage services come as part of the council’s plan to create a “cultural enterprise model”, meaning the services would make money for themselves and be more self-sufficient.
Councillor Colin Davie, Executive Member for Economic Development for Lincolnshire County Council. Photo: Steve Smailes
County councillor Patricia Bradwell, deputy leader of the authority, said the services need to keep “people interested and wanting to learn”.
Meanwhile, Councillor Colin Davie, executive member for economy and place, said heritage attractions across the county need to move with the times.
“It’s about attracting and inspiring,” he said.
“It’s about having places that are the heart of the community.
“The future is not going into somewhere and staring at walls, we have got to have a much better experience.”
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