The public has been asked to stay away from accident and emergency units at the Royal Lancaster infirmary and Furness general hospital unless they are seriously ill.
A spokesman at University hospitals of Morecambe Bay NHS foundation trust said the two sites were experiencing increased pressure in A&E and that it was “calling on the public to again help us”.
The trust issued a similar request in March with the chief operating officer, Foluke Ajayi, saying patients who were less seriously ill could be better treated elsewhere.
In a statement on Sunday, a spokesman for the trust said: “We do occasionally experience sudden increases in attendance which can impact on the time for patients to be seen, treated and either discharged or admitted. At the moment, patients are likely to experience long waiting times, whilst those who need urgent treatment are seen first.
“Please help us make sure our staff are free to treat those most in need, such as those who have a serious illness or injury. If you do attend, please be patient with staff who are doing their best in difficult circumstances.”
The spokesman described an emergency as a serious or life-threatening injury and condition, such as a suspected heart attack, acute confused state and fits that are not stopping, loss of consciousness, breathing difficulties, chest pain, head injuries or severe bleeding that cannot be stopped.
In December, the Care Quality Commission upgraded the University hospitals of Morecambe Bay NHS trust to “requires improvement” after it was placed in special measures in June 2014.