Line the bottom of a 9-inch springform pan with parchment paper and wrap the outside with aluminum foil to prevent leaks. Set aside.
Combine graham cracker crumbs, melted butter, sugar, and salt until the mixture resembles wet sand, then press firmly into the bottom and slightly up the sides of the prepared pan. Freeze for at least 15 minutes.
Beat softened cream cheese on medium speed for 2–3 minutes until completely smooth, then add sugar, sour cream, vanilla extract, and lemon juice and mix until well combined.
In a separate cold bowl, whip the cold heavy cream on high speed until stiff peaks form, about 3–4 minutes. Gently fold into the cream cheese mixture in three additions until no white streaks remain.
Spread the cheesecake filling evenly over the frozen crust using an offset spatula, then cover tightly with plastic wrap pressed directly onto the surface and freeze for at least 4 hours until firm.
Let ice cream soften for 10–15 minutes, fold in any mix-ins, then spread evenly over the frozen cheesecake layer. Cover with fresh plastic wrap and freeze for at least 6 hours or overnight until completely solid.
Beat heavy whipping cream, powdered sugar, and vanilla on high speed until medium-stiff peaks form, about 3–4 minutes. Refrigerate until ready to use.
Let the cake sit at room temperature for 5–10 minutes, then run a hot, dry knife around the inside edge and carefully release the springform pan sides.
Spread or pipe whipped cream over the top, add desired garnishes, and slice with a knife dipped in hot water and wiped clean between each cut. Serve immediately or return to the freezer until ready.