James Dobson, 15, was last seen at around 11.45am on Wednesday August 30 at an address on Ashton Drive, Lancaster.
Police say he may still be in the city, or he may have travelled to Bowness or Windermere, either alone or with a friend.
DS Trevor Walker, of Lancaster Police, said: “We are extremely worried about James and would like to hear from anybody who knows where he is, or thinks they’ve seen him.
“In particular we’d ask hoteliers in the Bowness and Windermere areas to study his photo carefully and get in touch if they believe they’ve seen him.
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“We would also urge James himself, if he sees this appeal, to contact us to let us know he is safe.”
James is described as white, of slim build, with short, dark-brown hair. He was last seen wearing a green Ralph Lauren polo shirt, grey North Face jogging bottoms, a navy, padded body warmer and black Lacoste trainers with white soles. He is also believed to be in possession of a gold, plastic, drawstring Footlocker bag.
Anybody with information is asked to contact police on 01524 596640 or if they fail to get an answer, 101, quoting log number 1699 of August 30.