Stir together the ricotta with a large pinch of salt and few grinds of pepper in a medium bowl. Cover and refrigerate until ready to use.
Prepare an outdoor grill for medium-high heat. Brush the grill grates with oil. Toss together the squash and zucchini slices, 1 tablespoon of the oil, 3/4 teaspoon salt and a few grinds of pepper in a large bowl. Grill the vegetables, turning once, until nicely marked and just tender, 2 to 3 minutes per side. Remove to the large bowl and toss with the juice of one of the lemon halves.
Brush the tops of the flatbreads with the remaining tablespoon oil and sprinkle with salt and pepper. Spread a quarter of the ricotta over each flatbread. Divide the grilled vegetables among the flatbreads. Transfer the flatbreads to the grill, cover and cook until the bottoms are slightly charred and crisp in spots and the ricotta is warm, 3 to 5 minutes.
Remove to serving plates and top each with a drizzle of oil, a squeeze of the other lemon half, some lemon zest and a drizzle of honey. Sprinkle with salt and red pepper flakes, then top with the fresh herbs.
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