Cook the pasta according to the package directions, making sure to liberally salt the water.
In a large skillet, brown the diced chicken, seasoning with salt and pepper. Once the chicken is browned, remove to a bowl with a slotted spoon and set aside.
In the same skillet, sautee the squash, zucchini, and minced garlic for about 30 seconds. Add the corn and sautee for another 30 seconds or so.
Add the chicken broth to the skillet, making sure to scrape the bottom to get up any brown bits. Add the diced chicken back to the skillet, as well as the lemon juice and some salt.
When the pasta is al dente (cooked but still slightly firm), add to the skillet along with about 1/2 Cup of reserved pasta water. Toss to combine everything.
Remove from the heat. Add 1/4 cup parmigian cheese and some chopped basil. Toss and taste for seasoning. Add more salt, cheese, lemon juice, or basil as needed.