Preheat oven to 400 degrees, with racks in upper and lower thirds. Soak eight 8-inch wooden skewers in hot water, 15 minutes. In a large bowl, stir together lemon juice, 3 tablespoons oil, thyme, and garlic. Season with salt and pepper. Add pork, onion, and squash and toss to coat.
Thread pork onto skewers and place on a rimmed baking sheet. Place onion and squash on another rimmed baking sheet. Place pork on top rack and vegetables on bottom rack and roast until pork is cooked through, about 30 minutes, flipping skewers and stirring vegetables halfway through. Remove pork and loosely tent with foil; continue roasting vegetables on bottom rack until tender and browned, 10 minutes.
Meanwhile, in a large skillet, heat 1 tablespoon oil over medium. Gradually add arugula and cook until just wilted, about 3 minutes; season with salt and pepper. To serve, divide pork skewers, vegetables, and arugula among four plates.