Pour the rice into a medium saucepan (nonstick works well). Add the milk, cream, butter, salt and 2 cups of water and stir to combine. Bring the mixture to a gentle boil over medium-high heat, then cover the pan, reduce the heat to low and simmer, stirring twice as it cooks, until all the liquid is absorbed and the mixture is creamy, 20 to 25 minutes.
Turn off the heat, add the sweetened condensed milk, vanilla and lemon zest and juice and stir. Return to the heat and cook for 5 more minutes, then turn off the heat again. Mix in the egg, stirring constantly.
Let the mixture sit in the pan for an additional couple of minutes, then serve it nice and warm with some grated lemon zest over the top.