Health bosses are warning people not to go to Lincoln County Hospital A&E this weekend unless absolutely necessary.
United Lincolnshire Hospitals NHS Trust said it was struggling to fill rotas due to a national shortage of doctors, and a reduced supply of agency staff.
Medical director Dr Neill Hepburn said the trust was working hard to "keep services running safely".
He urged people to "stay away" unless it was an emergency, or life-threatening situation.
Dr Hepburn said: "We are working hard to make sure we maintain a safe service for our patients by releasing senior staff from other specialities to help out in A&E over the weekend."
However, he added: "Please stay away from Lincoln A&E unless you need emergency health treatment - if it's not serious or life-threatening, please do not attend."
The trust said Boston's Pilgrim Hospital was also experiencing difficulties, but has so far managed to maintain minimum staffing levels.
Grantham and District Hospital's A&E unit has been closed overnight since last August because of a shortage of doctors.