Fill medium saucepan one quarter full with water. Bring water to a simmer over medium heat.
Combine egg whites, sugar, and cream of tartar in a heatproof bowl and place over saucepan. Whisk constantly until sugar is dissolved and whites are warm to the touch, about 4 minutes. Test by rubbing the mixture between your fingers. The mixture should feel smooth, if it feels gritty, the sugar is not completely dissolved yet.
Transfer mixture to electric mixer fitted with the whisk attachment, and whip, starting on low speed, gradually increasing to high until stiff, glossy peaks form, about 10-12 minutes. Add vanilla, and mix until combined.
Using a spatula, cover the lemon pie with the meringue. Cover completely to the edges. Now, using pulling up motions, create peaks with the meringue.
At this point you can use a torch to brown peaks, or place under the broiler for just a few minutes, watching carefully.
Keep pie in refrigerator until you serve. This meringue will stay set for a few days.