Thoroughly rinse rice and transfer to a large bowl. Pour enough water over the rice to cover by a few inches and soak for 1 hour; drain.

Bring a saucepan of water to a boil. Cook lima beans in boiling water until tender, 7 to 10 minutes; drain.

Bring a pot of water to a boil. Add salt and rice to the boiling water and cook until rice is partially softened, about 11 minutes; drain.

Season lamb with cinnamon, salt, and pepper.

Melt 2 tablespoons butter in a large skillet over medium-high heat. Cook and stir lamb in melted butter until completely browned, about 5 minutes. Use a slotted spoon to transfer lamb to a bowl. Cook and stir onion in skillet until translucent, about 7 minutes. Return lamb to skillet; add dill and cooked lima beans. Remove skillet from heat.

Melt 3 tablespoons butter in a large saucepan over medium-high heat; add 1 tablespoon hot water. Spoon about 1/3 the partially cooked rice into the saucepan. Layer about half the lamb mixture over the rice layer. Repeat layering 1/2 the remaining rice, the remaining lamb mixture, and finishing with the remaining rice. Cut the remaining 3 tablespoons butter into cubes and arrange atop the top rice layer.

Place a cover on the saucepan, reduce heat to medium-low, and cook until the rice is completely tender, about 30 minutes. Remove saucepan from heat and let the mixture cool for 10 minutes before serving with yogurt.