Preheat grill pan or grill.
Split the sausage links down the middle so they open up like a book. Drizzle them with a bit of EVOO and place them onto the hot grill. Cook about 10-15 minutes, turning every once and a while so that they cook evenly and get nice grill marks on all sides.
While the sausages are cooking, combine the mozzarella, tomatoes, red peppers, red onion, basil and arugula in a large mixing bowl and toss with the lemon juice, 3 tablespoons EVOO, salt and pepper.
When the sausages are done cooking, slice them into bite-size pieces and toss them into the bowl with the veggie mixture.