Is it safe to half cook a lamb roast and the recook the roast the next day? 
It depends on exactly what you mean by ‘half cook’ The problem comes if you warm it up, but don’t bring it up to a hot enough temperature to kill off any dangerous microbes. If you then cool it back off and warm it again, then you’re giving the microbes a significantly longer period of time to multiply and produce toxins.  (As they have the initial warning period, the cooling until they go dormant, and then the second warning period) You need the initial cooking to take the meat up to the minimum safe temperature for the meat, or to pasteurize it by bringing it up to sufficient temperature and holding it there for sufficient time to kill pathogens. (See Balwin’s charts for sous vide pasteurization, but keep in mind that you’re not doing sous vide) You can then cool it off and bring it back to eating temperature the next day.  But the process of heating it twice can potentially dry out / overcook the meat.  I prefer to slice it up, and place it into hot gravy or other sauce to warm up slowly. 