For the dough, heat the almond milk and oil in small saucepan set over medium heat and set aside.
In the bowl of a food processor, pulse the sugar until it is finely ground. Add the white whole-wheat flour, yeast, and salt and pulse two or three times to combine. With the machine running, slowly put the hot almond milk through the feed tube. Add the whole-wheat flour ¼ cup at a time, pulsing until the dough pulls away from the sides of the bowl.
Transfer the dough to a floured work surface. Knead for 4 to 5 minutes, and then shape into a ball. Put the dough in a large oiled bowl and cover loosely with plastic wrap. Let it rise in a warm place until doubled in size, 1 to 1 ½ hours.
Preheat the oven to 425 F. Dust 2 baking sheets lightly with flour and set aside.
Punch down the dough and divide it into 4 equal pieces. Lightly dust a cutting board with flour and roll each piece out into a circle that is ⅛ inch thick. Transfer 2 crust to each of the prepared baking sheets and prick the surfaces all over with a fork. Let it rest for 10 minutes.
Bake the crusts until golden brown, 12 to 15 minutes. Set aside.
For the toppings, heat the oil in a large skillet set over medium-high heat. Add the mushrooms and cook, stirring, until golden brown, about 4 minutes. Remove the pan from the heat and stir in the lemon juice and season to taste with salt and pepper.
Assemble the pizzas by spreading the hummus over the crusts and arranging the arugula, mushrooms, and tomatoes on top. Serve immediately.