Bring all refrigerated ingredients to room temperature. Grease a 5 x 9-inch loaf pan.
In the bowl of a stand mixer, combine eggs, oil, and lemon juice. In a large measuring cup, combine water, 1 tablespoon sugar, and yeast; let stand for 5 minutes, or until foamy. In a medium bowl, combine tapioca starch flour, brown rice flour, dry milk powder, xanthan gum, salt, and 3 tablespoons sugar. Add yeast mixture to the egg mixture, then slowly add dry ingredients a little at a time until completely incorporated. Mix batter on high speed for 31/2 minutes, then pour into prepared pan.
Cover bread with foil and place in a cold oven. Set a pan of hot water on a lower shelf underneath the bread. Leave for 10 minutes with oven door closed. (This will cause the tread to rise quickly.) Remove bread from oven (do not uncover) and place in a warm place in the kitchen.
Preheat oven to 400 °F Bread will continue to rise as oven preheats.
Uncover bread and bake for 10 minutes to brown the top. Cover bread with foil and continue to bake bread for 30 minutes.