Lamb half cook then recook next day

Probably (famous last word)

(curious) what is the reason you want to do it in 2 stages ? Lamb roast usually does not take a long time to cook.

You could quickly roast/brown it at high temperature to have a crust.

Quickly cool it down in the fridge, and the next day, continue cooking up to temperature.

I'm not expecting this to result in the best roast, but it should be feasible,