Set a rack in the lower third of the oven and heat to 400°F (205°C). Fit the cold pie crust into a 9-inch pie plate, fold and crimp the edge, and freeze for 15 minutes to firm.
Line the chilled crust with parchment and fill with pie weights or dried beans. Bake 12 minutes. Carefully remove the parchment and weights, dock the bottom with a fork, reduce the oven to 375°F (190°C), and bake 10–12 minutes more until lightly golden. Cool on a rack while you prepare the filling. Keep the oven at 375°F.
For the filling, whisk together sugar, cornstarch, salt, and turmeric in a medium saucepan. Gradually whisk in the water and lemon juice until smooth with no dry pockets.
Cook over medium heat, whisking constantly, until the mixture turns glossy, thick, and begins to bubble slowly, 5–7 minutes. Remove from the heat and let it stand 2 minutes to cool slightly.
In a separate bowl, whisk the egg yolks until even in color. Slowly whisk about 1/2 cup of the hot lemon mixture into the yolks to warm them, then scrape the yolk mixture back into the saucepan. Return to medium heat and cook, stirring, for 90 seconds after the first big bubbles appear. Off heat, whisk in the butter, lemon zest, and lemon extract (if using). Immediately pour the hot filling into the warm crust and smooth the top. Set the pie on a baking sheet to catch drips.
Make the Swiss meringue: Bring 1 inch of water to a bare simmer in a saucepan. In a heatproof mixer bowl, combine egg whites, sugar, cream of tartar, salt, and cornstarch. Set over the steam (bowl should not touch water) and whisk constantly until the sugar is dissolved and the mixture reaches 160°F (71°C), 3–5 minutes.
Transfer the warm whites to a stand mixer (or use a hand mixer) and whip on high speed until the meringue is thick, glossy, and forms stiff peaks, 4–6 minutes.
While the lemon filling is still hot, pile the meringue onto the pie, anchoring it to the crust all around so there are no gaps. Swirl and peak the top for texture.
Bake at 375°F (190°C) until the tips are nicely browned, 8–12 minutes. Cool the pie on a rack for 1 hour, then refrigerate uncovered 2–3 hours before slicing.