1 pint cherry tomatoes, halved
1. Line 3 rimmed baking sheets with paper towels and arrange zucchini in a single layer on top. Sprinkle with 1 1/2 t. salt and set aside 30 minutes. (This is an important step if you don’t want a soupy lasagna in the end.)
2. Meanwhile, heat a grill to medium (350° to 450°). Heat 1 T. oil in a medium frying pan over medium heat. Add shallot and garlic and cook, stirring constantly, until beginning to brown, about 2 minutes. Add corn and thyme and cook until corn is just hot, 2 to 3 minutes. Transfer to a medium bowl. Stir in ricotta, half of parmesan, the egg, basil, chives, pepper, and remaining 1/4 t. salt.
3. Preheat oven to 375°. Press water out of zucchini with more paper towels and remove all paper towels from baking sheets. Brush zucchini all over with remaining 2 T. oil. Grill half of zucchini, turning once, until grill marks appear, 2 to 4 minutes; transfer to rimmed baking sheets as cooked. Repeat with remaining zucchini.
4. Butter bottom of a 9- by 13-in. baking dish with 1/2 T. butter. Arrange a quarter of zucchini ribbons crosswise in bottom of dish, overlapping slightly. Evenly spread a third of corn-ricotta mixture over zucchini. Sprinkle with a handful of tomatoes. Repeat process 2 more times, ending with zucchini. Sprinkle remaining parmesan on top and dot with remaining 1 T. butter.
5. Bake until lasagna turns golden brown, about 45 minutes, rotating dish halfway through for even browning. Let rest 20 minutes before serving.