Preheat the oven to 350F. Place your unbaked pie crust in your pie pan and set it aside.
In a large mixer bowl, beat the eggs until just combined. In a small mixing bowl, whisk together the sugar, flour, and nutmeg. Add the sugar mixture to the eggs and blend. Add the butter, applesauce, vanilla and lemon juice, and combine gently being careful not to overmix; you want to avoid adding to much air to the batter.
Pour the filling into the pie shell and bake for 45 minutes or until the top of the pie is golden brown and set in the center. Remove from the oven, cool about 30 minutes on a rack, and serve slightly warm.