With an electric mixer, beat the egg yolks until they become light-colored and thick. Beat in the condensed milk for about a minutes. Then add lemon juice and lemon zest, and blend well. Pour into cooled pre-baked pie shell.
Make a meringue by beating egg whites in a completely clean, grease-free bowl (the best possible is a copper bowl) with cream of tartar at high speed, until peaks begin to form. Add the sugar and vanilla, and beat until stiff but not dry. Spread meringue on top of pie.
Bake pie at 350 degrees for 10 minutes, or until top is lightly brown. Chill several hours before serving.