Bring a large pot of water to a boil; season with salt.
Build the skewers by adding 1 mushroom, 1 piece of chicken, 1 red onion chunk, 1 zucchini round, 1 more piece of chicken, and 1 cherry tomato. Continue in this fashion until all the skewers are completely filled. Place the completed skewers in a shallow wide container and set aside.
Cook pasta 1 minute less than package directions. Toss with 1 tablespoon olive oil and set aside to cool down.
Heat grill to high. Season the skewers with salt and black pepper, then drizzle with 2 tablespoons of olive oil. Cook the skewers on the grill for 4 to 5 minutes; remove them from the heat and set aside when cooked.
Add the remaining olive oil and the garlic to a small skillet and heat it over the grill for 1 minute. Add the pasta to a medium-size grill basket and place it on the grill. Cook about 5 minutes, until the pasta turns golden and starts crackling then remove from heat. Toss pasta with the olive oil and garlic mixture, basil, and oregano.
Top with the grilled skewers and drizzle with lemon juice.