Why isn't it "Han vil gerne leje en båd"?
both are correct
but Duo does not accept it!!!
Is it a case of "gerne" not being necessary for you to understand the sentence
'Gerne' expresses a bit more politeness I suppose. It is perhaps more correctly translated to 'he would like to rent a boat'.
I think it is more common to add 'gerne', especially in first-person sentences.