Preheat oven to 450º F.
Combine flour, cornmeal, millet, ginger, baking powder, salt, and lemon zest in a medium bowl.
Whisk together water and olive oil. Pour liquid into the dry ingredients in a steady stream while stirring with a wooden spoon. Continue stirring until a dough forms. Gently knead the mixture until it is smooth, about 5 to 6 times.
Divide the dough into three pieces. Working with one piece at a time, roll dough as thinly as you can between two pieces of parchment paper (lift the paper on each side and reapply it once or twice during rolling to prevent sticking).
Remove the top piece of parchment paper and scatter salt over the surface. Press salt down gently with the rolling pin to help it adhere.
Using a pizza cutter or sharp knife, slice the dough into diamonds. Leaving the crackers intact on the bottom sheet of parchment paper, slide it onto a baking sheet. Repeat with remaining dough.
Bake crackers until pale golden and slightly browned around the edges, about 10 to 12 minutes. Cool and serve.
If not serving right away, cool crackers completely and store in an airtight container for up to two days. Refresh crackers in a warm oven.
