Add the rice, milk, and salt to a medium saucepan. Bring to a gentle simmer, stirring frequently.
Reduce the heat and cook for 20–25 minutes, until the rice is tender and most of the milk has been absorbed. Stir in the butter and let the rice cool.
In a large mixing bowl, whisk together the eggs and sugar. Add the ricotta cheese, vanilla extract, lemon zest, and optional cinnamon. Mix until combined.
Gently fold the cooled rice into the ricotta mixture until evenly distributed.
Preheat the oven to 350°F (175°C). Place the pie crust into a 9-inch pie dish.
Pour the filling into the crust and smooth the top with a spatula. Place the pie dish on a baking sheet.
Bake for 55–70 minutes, until the crust is golden and the filling is set with a slight wobble in the center.
Remove the pie from the oven and let it cool on a wire rack for 2–3 hours before slicing.
Serve at room temperature or chilled. Refrigerate any leftovers.