You need to register as a food business with your local authority first things first, who will come out and ask how you’re keeping the meat cold, storing before it’s picked up, handling it etc. if you collect it from the butcher and deliver straight away and it’s all vac packed it’s relatively straight forward. Have buyers lined up before you kill the lambs, primed to collect or be delivered on a day/time.
We have a large commercial walk in chiller to keep things cold, just take temps at regular intervals, have a back up plan if things to wrong. I don’t think you can use your kitchen fridge. Freezing the meat makes things more difficult and most people prefer fresh.