Lambs get sent off when they're 'finished'. They're 'finished' when they have the right amount of flesh covering their bones. Have a read of 'Understanding Lambs and Carcases' from Eblex - near the bottom of
this pageHow long a lamb takes to finish depends on a lot of things - breeding, the ground it's on, its mother and her milk (which also depends on her breeding and the ground
she's on), the weather, a host of things.
Some lambs finish in 12 weeks or even less, never having needed a dose of anything nor a speck of cake. Others, of the same breeding, may need 6 months or more, and some cake, to achieve the same end result.
Some breeds don't mature in their first year, so are finished as 'hogget' at 14-16 months old.
And all points in between.
Some farms finish all their lambs, selling them as fat either in the ring or direct to slaughter. Other farms finish some, those which finish before the grass starts to die back at the end of the summer, and sell the rest as 'stores'. Dairy farms often buy store lambs at the end of the summer, to graze the pastures over the winter while the cattle are housed. When the lambs are finished they get sent off for a cash crop, the pastures are in good order and 'clean' (all the cattle bugs eaten up and neutralised, is the theory), ready for the cattle to come out in spring.