Is this a menu for the USA or the UK?
USA pork, chicken, smoked sausage with beans, slaw and potato salad.
UK lamb, pork, chicken, smoked sausage with beans, slaw and potato salad.
Cook NZ shoulder of lamb, the same as you'd cook pork shoulder, but with EVOO slather and garlic, rosemary and thyme in slits every inch to inch and a half, a sliver of garlic in one third of the slots, sprig of rosemary in one third, or the thyme etc.
The difference is that for the most part, lamb in the USA is not a cheap meat like it is or can be in the UK.
"There is no such thing as a little garlic." A.Baer