I had one injured a year or two back and separated her into her own run full time for at least 3 weeks if not 4, which is how long it took her to fully recover. I would give your one a bit longer before culling, given her age and likely productivity.
But then I have a young CL hen about 7-8 months old which only has one leg and has permanent separate accommodation from the flock tho only separated by mesh and socialises well enough within that safety zone. She laid her first (blue) egg today and I wasn't sure it'd not be crushed when she got up, but I'm delighted it looks like she's going into production and if she lays, she's viable lame or one legged or no, as far as I'm concerned