Why is it called Shah Plov?

The name evokes a royal or kingly presentation, appropriate to the dramatic crown-like lavash shell.

Can I assemble it ahead?

Prepare the filling and rice ahead, but line and bake the lavash shortly before serving for the crispest crust.

Rinse and soak rice for 30 minutes. Boil in well-salted water until about 70 percent cooked, then drain.
Melt 50 g butter in a pan. Brown lamb, add onions, salt and pepper, then cook gently with a splash of water until tender, about 40 minutes.
Add chestnuts, apricots and raisins to the lamb for the final 10 minutes. Keep the mixture relatively dry.
Heat oven to 180°C. Brush a deep round ovenproof pot generously with melted butter.
Line the pot with overlapping lavash, allowing long edges to hang over the rim. Brush each sheet lightly with butter.
Add half the rice, spoon over some saffron infusion and butter, then spread the lamb mixture. Cover with remaining rice, saffron and butter.
Fold the lavash over the top to enclose the rice completely. Brush with more butter.
Bake for 50 to 60 minutes until the crust is crisp and golden.
Rest 10 minutes, invert onto a large platter and cut open at the table.