The 20-year-old could not make a first-team appearance for Bolton due to restrictions imposed by the EFL.
Signed after leaving Blackburn Rovers' youth team in summer 2016, Lavelle was told in July he would not be given a new contract with the Trotters.
"Sam is young but has a lot of promise. We are looking forward to working with him," boss Jim Bentley said.
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Morecambe have signed former Bolton Wanderers youth defender Sam Lavelle on a one-year contract.