Prepare the Marinated Cherry Tomatoes: Stir together all Marinated Cherry Tomatoes ingredients in a large bowl. Cover and chill 8 hours or overnight.
Prepare the Salsa Verde: Stir together all Salsa Verde ingredients in a bowl until combined. Cover and chill until ready to serve.
Prepare the Grilled Pompano: Preheat grill to medium-high (about 450°F). Rinse pompano inside and out, and pat dry with paper towels. Stuff cavity of each fish with half of lemon slices and thyme sprigs. Brush each fish with 1 1/2 teaspoons olive oil, and sprinkle inside and outside of fish with salt and pepper. Place fish on oiled grates; grill, uncovered, turning once, until skin is charred and flesh is white and opaque, about 14 to 20 minutes. Top grilled fish with Salsa Verde and Marinated Cherry Tomatoes, and serve.