Preheat oven to 425°F and line a baking sheet with parchment paper.
Cut the summer squash into 1-inch chunks, slice the asparagus into 2-inch pieces, and remove the kernels from the corn.
Add vegetables to the baking sheet. Drizzle with the olive oil and sprinkle with the salt and pepper. Toss gently to coat.
Roast for 20 minutes, until vegetables are tender and lightly browned.
While the vegetables roast, cook the pasta according to package directions in well-salted water (about ½ teaspoon salt).
Add the frozen peas to the pasta during the last 5 minutes of cooking. Check pasta for doneness, as peas may slightly extend cooking time.
Before draining pasta, reserve ⅓ cup of pasta water. Drain the pasta and peas, then rinse briefly under cold water and shake well to dry.
In a large mixing bowl, whisk together the reserved pasta water, pesto, and lemon juice.
Add the pasta, roasted vegetables, and chopped artichokes. Toss until everything is evenly coated.
Season with additional salt and pepper as needed. Serve warm or refrigerate for at least 4 hours to serve chilled.