The historic building's west entrance is under used by visitors and will be shut for five years starting on April 1 this year.
But business officials say the closure will dramatically reduce footfall for shops in the Union Road area, which is also home to The Lawn.
Uphill business owner Jonathan Pass said the closure could be the "final nail in the coffin" for some small traders in the area. Mr Pass added he was frustrated at the lack of warning from the authority on the changes.
Lincolnshire County Council made the closure decision.
Its executive member for economic development and culture, Councillor Eddy Poll, said work to build a heritage skills centre within the historic landmark's grounds later this year would have required the entrance to be closed any way.
Cllr Poll added that the east gate entrance was the busier of the two, with 90 per cent of visitors choosing this option.