Heat the oven to 325°F. Set the prepared crust, still in its pie pan, on a rimmed baking sheet.
Beat the room-temperature cream cheese and mascarpone on medium-low speed until smooth. Mix in the sugar, scraping the bowl.
Mix in the eggs one at a time on low speed, then the vanilla, optional lemon juice, sour cream or yogurt, and salt; avoid whipping in excess air.
Pour into the crust. Bake for about 40–55 minutes, until the edges are set and the center reaches 160°F; the center can still wobble gently but should not look liquid. Begin checking at 40 minutes.
Cool on a rack for about 1 hour, then refrigerate at least 4 hours before slicing. This filling contains eggs and must be baked; do not use it as a no-bake filling.