Preheat oven to 375 degrees. Line baking sheets with parchment paper or silicone baking mats.
In a large bowl, whisk together 9 cups of the flour, baking soda, and cream of tartar; set aside.
Using an electric mixer on medium speed, blend the eggs and sugar until thoroughly combined, 1 to 2 minutes. Add the margarine and blend well. Add the lemon zest and juice and mix until smooth and combined.
Reduce the mixer speed to low and gradually add the flour mixture alternatively with the milk until just combined. Using a rubber spatula, mix in the chocolate chips.
Turn the dough out onto a lightly floured surface and divide into 8 pieces. Dust the dough lightly with flour if it's too sticky to handle. Gently shape the dough into logs that are approximately 10 inches by 2 inches, then transfer to the prepared baking sheets (depending on the size of your sheets, you should be able to bake two or three loaves per sheet).
Brush the tops with the beaten egg white and sprinkle with sugar. Bake for 25 to 30 minutes, or until golden brown and tester comes out clean. Allow to cool completely before slicing. The soft biscotti can be wrapped in plastic wrap and stored at room temperature for up to 1 week. You can also add a layer of aluminum foil and freeze for up to 2 months.
While you may be tempted to substitute butter for the margarine, I would caution against it, as it may change the taste and texture of the dough.