Preheat the oven to 375 degrees F. Heat 2 tablespoons olive oil in a large Dutch oven or pot over medium-high heat. Add the celery, carrots, onion, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables are softened, 7 minutes.
Add 6 cups water, the chickpeas, tomatoes, 2 teaspoons cumin, 1 teaspoon coriander and 1/2 teaspoon salt. Bring to a simmer and cook, stirring occasionally and slightly mashing the chickpeas with the back of a spoon, until the soup thickens slightly, about 20 minutes. Season with salt and pepper.
Meanwhile, slice the pitas into thin wedges. Toss with the remaining 2 tablespoons olive oil, 1 teaspoon cumin, 1/2 teaspoon coriander and 1/2 teaspoon salt. Spread in a single layer on a baking sheet. Bake until golden and crisp, 8 to 10 minutes.
Stir the lemon juice into the soup just before serving. Top with cilantro and the pita chips.