Cut off the ends of the zucchini and slice each lengthwise, into quarters or eighths, depending on the size of the zucchini and your preference.
Place the zucchini spears into one or two large resealable plastic bags. Add the olive oil, salt, pepper, lemon zest, and juice of two lemons to the bag(s). Seal the bag(s) and gently shake and/or massage to mix the marinade until evenly dispersed and the zucchini is coated. Set aside for as little as 5 minutes, or up to 20 minutes, to marinate.
Preheat the grill to medium or medium-low heat. Grill the zucchini on all three sides until tender, but don't let it burn, about 5 minutes per side. Remove each from grill when done.
Combine the lemon zest and kosher salt for the lemon salt. Use a knife to cut the zest and salt together until well combined. Sprinkle the grilled zucchini with lemon salt and serve warm.
Cooking time may vary depending on your grill and the size of the zucchini.