Using the large holes of a box grater, grate zucchini into a medium bowl. Add the salt, lemon zest, chopped parsley, garlic, pepper, and eggs. Mix well to combine. Slowly add flour, stirring so no lumps form.
Heat 2 tablespoons olive oil in a large saute pan over medium-high heat until the oil sizzles when you drop a small amount of zucchini mixture into the pan. Carefully drop about 2 tablespoons zucchini mixture into pan; repeat, spacing fritters a few inches apart.
Cook fritters until golden, 2 to 3 minutes. Lower heat to medium. Turn fritters, and continue cooking until golden, 2 to 3 minutes more. Transfer fritters to a plate; set aside in a warm place. Cook remaining zucchini mixture, adding more oil to pan if necessary. Garnish with parsley sprigs and lemon wedges, if desired; serve.