Officials at United Lincolnshire Hospitals Trust and neighbouring health authorities urged patients to practise self care and only go to A&E if it is an emergency.
Simon Evans, director of operations at the trust, said the trust and its partners have devised a winter plan in an effort to cope.
Lincolnshire’s emergency departments have seen a spike in demand in recent months with more people appearing at A&E unwell.
Mr Evans said the trust expects to see that demand “sustained” over the festive months.
“We have seen a sustained increase since November,” he said.
“We are expecting that to continue and our plans, which are based on previous years, expect to have that sustained pressure over the remainder of this year.
“We aren’t expecting to get significantly more in terms of the norovirus, we have had a significant amount of that already, but we are expecting flu to increase.”
He added that the trust was prepared for the demand in terms of staff.
Ruth Cumbers, who leads urgent and emergency care across Lincolnshire NHS, said the increase in demand at A&E was “unprecedented” but added that measures were in place for winter.
Officials have urged patients who feel unwell to check online services, such as NHS 111, as a first point of call.
The service will ask questions on symptoms and be able to direct people to the right service.
Mr Evans said NHS 111 will help solve the “majority” of cases, but will also be able to signpost people to A&E if they need it.
“It will always be able to catch patients who are acutely unwell,” he said.
“It will be able to direct them to the most appropriate place. At that point it could be conversations with NHS 111 or with a practitioner as part of the Lincolnshire clinical assessment service.
“For most people that will be able to solve what is going on with them over winter.”
Meanwhile, urgent treatment centres will also be available in Louth, Skegness, Lincoln and Boston to treat people who need urgent care, but not necessarily life threatening.
The trust has seen high demand over recent months at A&Es, with 15,139 patients attending emergency departments across the county in October alone.
ULHT has not met its waiting time targets for A&E for half a decade.
Earlier this week, union bosses said the trust was “on its knees” and urged the government to take action.