Bring a large pot of salted water to a boil, then add the pasta and cook until just al dente, following package instructions. Drain and rinse thoroughly under cold water until completely cooled, then toss with a little oil to prevent sticking.
While the pasta cools, chop the cherry tomatoes into halves, thinly slice the cucumbers, and soak the red onion slices in cold water for about 10 minutes to mellow their sharpness. Drain and set aside.
In a large mixing bowl, combine the cooled pasta, halved cherry tomatoes, sliced cucumbers, and drained red onion. Toss everything gently to distribute evenly.
Add the pesto and lemon juice to the bowl, then stir well until all the pasta and vegetables are evenly coated with the fragrant, herby sauce.
Sprinkle in the freshly grated Parmesan cheese and toss again to incorporate the cheesy bits throughout the salad.
Cover the bowl with plastic wrap and refrigerate for at least an hour to let the flavors meld and the salad chill thoroughly.
Before serving, give the salad a good stir to refresh the pesto coating and redistribute any juices. Serve chilled, enjoying the crisp vegetables and fragrant, herbaceous pasta.