Put the potatoes in a large pot with enough cold water to cover by 2 inches; add a large pinch of salt and bring to a boil. Cook until the potatoes can just be pierced with a fork, 10 to 25 minutes depending on their size. Drain and let them sit to dry out until they're cool enough to handle. Slice the potatoes as thin as you can manage, at most 1/4-inch-thick; transfer the potato slices to a bowl and gently toss with the lemon juice and zest, 4 tablespoons oil, and lots of salt and pepper.
Put the remaining 3 tablespoons oil in a large skillet over medium-high heat. When it's hot, add some of the fennel in a single layer, taking care not to crowd (you'll probably have to work in batches) and sprinkle with salt and pepper. Cook, stirring occasionally, until lightly browned and tender, 3 to 5 minutes. Transfer to a plate and repeat with the remaining fennel.
Return all the fennel to the skillet and add the wine. Reduce the heat so the liquid bubbles gently and cook, stirring occasionally and scraping any browned bits from the bottom of the pan, until the fennel is quite tender and the pan is dry, 5 to 10 minutes. Taste and adjust the seasoning.
Heat the oven to 500 degrees F and put the rack in the lower third, with the pizza stone if you're using one.
Prepare the pizza dough according to the recipe directions. Top each pizza with half the potato slices (it's okay if they overlap a bit), then scatter with half the braised fennel. Put one baking sheet into the oven or slide the pizza on its parchment onto the stone. Bake until the crust is crisp, anywhere from 5 to 12 minutes. Chop the fennel fronds, sprinkle half over the pizza, drizzle with olive oil, slice and serve. Bake the second pizza while you eat the first.
Whole Wheat Pizza Dough:
Grease a large bowl with olive oil. Put all-purpose flour, whole wheat flour, instant yeast, and salt in a food processor. With the machine running, gradually add olive oil and 1 cup water, taking care not to overmix. Continue to run the machine, slowly adding 1/2 cup more water, until the dough forms a ball and is slightly sticky to the touch, about 30 seconds. If it's still dry, add 1 tablespoon water and process for another 10 seconds, but make sure the dough stays only a little sticky. (Unlikely, but if the mixture is too sticky to handle, add flour 1 tablespoon at a time and process for 10 seconds.) Transfer the dough to a floured work surface and knead by hand until you have a smooth, round ball, just a few seconds. Put the dough in the prepared bowl, turn to coat in the oil and cover with plastic wrap; let rise until doubled in size, 1 to 2 hours.
Cut the dough into 2 pieces. Cover the dough with plastic wrap or a towel and let rest until it puffs slightly, 20 minutes or so.
Cut 2 pieces of parchment the size of large rimmed baking sheets (or pizza stone if you have one). Line 2 baking sheets with the parchment and, using floured hands, transfer one piece of dough to the parchment with the help of a spatula or pastry blade; put the other piece of dough on the second sheet. Let the dough sit for a few minutes; this will relax the dough and make it easier to roll out. Lightly press or roll each dough ball into the pan to about 1/4-inch thickness, flouring the dough only as necessary to prevent sticking. (If you're using a pizza stone, roll or pat out the dough onto parchment, 1/4-inch-thick, then transfer to a peel.) Press gently on the dough to readjust and flatten before topping.