Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Whisk the flour, baking soda, cream of tartar and salt in a medium bowl; set aside.
Beat the butter, sugar and lemon zest in a large bowl with a mixer on medium-high speed until light and fluffy, 3 minutes. Beat in the eggs, one at a time, then beat in the lemon juice and vanilla. Reduce the mixer speed to low; beat in the flour mixture in two batches until combined. Stir in the white chocolate chips with a wooden spoon.
Drop heaping tablespoonfuls of dough about 2 inches apart on the prepared pans. Bake, switching the pans halfway through, until the cookies are just golden around the edges, 10 to 12 minutes. Let cool 3 to 5 minutes on the baking sheets, then transfer to a rack to cool completely.