The Kemp's ridley turtle was one of two found on beaches near Formby, Merseyside, and Cumbria's Walney Island on 22 December.
The reptile found in Merseyside died soon after, but the other was being looked after at the Lake District Coast Aquarium in Maryport.
Aquarium owner Mark Vollers said it had struggled to feed itself.
The turtles were believed to be from the Gulf of Mexico 5,000 miles (8,000 km) away and were among a small number which washed up on British and European shores last month.
Mr Vollers told BBC Cumbria: "We thought we had a 50/50 chance, which would've improved if it had started feeding.
"It was getting some sustenance in other ways but not really enough to recover.
"We were following a strict agreed protocol arrived at after consultation with vets here and in other countries - people who have experience of this species of turtle."
The turtle, possibly aged about 20, is now with a specialist vet who will determine the cause of death.
Source: World Wide Fund for Nature (WWF)
A turtle, thought to be from the Gulf of Mexico, that washed up on a Cumbrian beach has died.