Lop off the tops and bottoms of the zucchini and quarter them lengthwise. Place in a very large resealable plastic bag (or two regular-size bags). Drizzle in the olive oil, then add 1 teaspoon salt,1 teaspoon pepper, 1 tablespoon lemon zest and the lemon juice. Seal the bag and smoosh everything around a bit so that the zucchini is coated. Set aside for 15 to 20 minutes to marinate.
Preheat a grill to medium. Grill the zucchini, turning, until nice and tender, being careful not to burn it, 12 to 15 minutes. Remove the zucchini to a plate as it gets done.
Pile up the rest of the lemon zest on a cutting board and sprinkle 1 tablespoon salt on top. Use a knife to chop the salt and zest together until it becomes lemon salt. Add more salt if it needs it. Sprinkle the lemon salt over the grilled zucchini.