In a medium bowl, combine the onion with 1/2 cup of the vinegar, 1 1/2 teaspoons of salt and the water. Let stand until the onions are lightly pickled, 3 to 4 hours. Drain.
Meanwhile, preheat the oven to 400°. Line a large rimmed baking sheet with parchment paper. Arrange the pancetta on the baking sheet, cover with another sheet of parchment and another baking sheet. Bake for about 30 minutes, until the pancetta is browned and crisp. Remove the top baking sheet and parchment paper and let the pancetta cool.
In a large skillet, heat 2 tablespoons of the olive oil. Add the carrot, parsnip, 4 thyme sprigs and a pinch of crushed red pepper. Season with salt and cook over high heat, stirring occasionally, until tender, about 3 minutes. Scrape the vegetables onto a plate and discard the thyme.
Add 2 tablespoons of the olive oil to the skillet along with the squash, celery root, the remaining 4 thyme sprigs and another pinch of crushed red pepper. Season with salt and cook over high heat, stirring occasionally, until the squash and celery root are tender, 5 minutes. Discard the sprigs. Return the carrot and parsnip to the skillet. Stir in the remaining 1/4 cup of vinegar and 1/2 cup of olive oil.
Arrange the lettuce on plates. Top with the warm vegetable vinaigrette, pickled onions and crispy pancetta. Serve right away.