Heat the grill to medium, then cut the zucchini in half crosswise and slice it lengthwise with a mandolin no thicker than 1/4 inch. Thin, even strips cook off moisture more evenly and stack more neatly than thick or uneven slices.
Grill the zucchini slices for 3 to 5 minutes per side until tender, then transfer them off the heat and set them aside. The slices should be flexible and lightly marked, with much of their surface moisture cooked away but no mushiness.
Place a large saute pan over medium heat and cook the ground beef for 7 to 10 minutes, breaking it up as it browns, then add 3/4 tsp of the salt, the pepper, the red pepper flakes, and the tomatoes. The beef should be fully cooked and crumbly, and the sauce should look a little thicker rather than thin or greasy.
Stir together the ricotta, parmesan, basil, egg, garlic, and the remaining salt in a large bowl until evenly combined. The mixture should look thick and spreadable, not loose or watery.
Heat the oven to 350 °F and brush a 9x13 inch glass or ceramic baking dish with the oil, then layer one third of the zucchini, one third of the ricotta mixture, one third of the meat sauce, and one quarter of the mozzarella; repeat this layering two more times and finish with the remaining mozzarella called for in the method. Keep the layers even and leave a small border around the edge so the sauce can bubble without spilling over too much.
Bake for 30 minutes, then let the lasagna stand for 10 minutes before serving. It’s ready when the dish is bubbling and hot, and the short rest helps the cheese and filling settle into cleaner slices.