Councillor Colin Davie, executive member for economy and place at the authority, said that new ministers will need to work hard to “ensure stability” for the farming sector.
The National Audit Office (NAO) said farmers had been left unable to plan for the future after losing subsidies they would receive as part of the EU Common Agricultural Policy.
Farmers and landowners received £3.5 billion in payments from the Common Agricultural Policy last year, according to the BBC.
Five Lincolnshire businesses received more than £12 million in subsidies.
Councillor Davie, who voted to leave the EU, said Lincolnshire had some of the “best farming land in the country” and the sector needs to be paid “fairly”.
“It’s very clear to me and to the government that we need a situation where British farmers are properly supported and paid fair prices for the products they produce,” he said.
“Lincolnshire has some of the best farming land in the country and its farmers are some of the most industrious, creative and produce some of the best products in the country.
“I want to make sure that their businesses can thrive in the future. It is about making sure that in the immediate period around October onwards and the transition period after we leave the EU that no farmers suffer.”
He added that the subsidy level given to farmers should remain at the same rate through a transition period, should a withdrawal deal be agreed.
Councillor Davie said the government also needed to ensure that no farmers “suffered” should the UK leave without a deal.
Environment Secretary, Michael Gove MP, set out proposals last year where the government would guarantee current funding levels until 2022.
But, the NAO said the government has not told farmers exactly how the new system would work.
The government said subsidy levels would be maintained until the next general election.