Clean the grill grates thoroughly and lightly oil them to prevent the zucchini from sticking. Dip a folded paper towel in cooking oil, then use tongs to rub it across the grates.
Preheat the grill to medium-high (around 375-400°F). If you're using a charcoal grill, light the coals evenly and wait until they glow.
Wash the zucchini under cold running water. Pat it dry with a paper towel or a clean kitchen towel.
Place the zucchini on a cutting board. Trim the stems and bottoms. Cut the zucchini in half crosswise. Stand each half upright on a cutting board and cut it in half lengthwise.
Repeat this process with the other half of the zucchini. Add to a large plate or baking tray.
Whisk together olive oil, salt, black pepper, minced garlic, chopped basil, dried oregano, and lemon juice in a small bowl. Brush the zucchini with the olive oil mixture, coating both sides.
Place the zucchini slices on the preheated grates and cook for 3-4 minutes per side−at least until they are tender and have nice grill marks.
Take the zucchini off the grill and serve immediately. Garnish with additional chopped basil, Parmesan cheese, and red pepper flakes, if desired.