Heat 1 1/2 inches of vegetable oil in a medium Dutch oven or heavy-bottomed pot over medium-high heat until a deep-fry thermometer registers 350 degrees F.
Meanwhile, put the flour in a shallow dish. Lightly beat the eggs with 1/2 cup water in another shallow dish. Whisk the cornmeal, Cajun seasoning and thyme in a third dish. Dredge the okra in the flour, shaking off the excess. Dip in the beaten eggs, then dredge in the cornmeal mixture. Fry, turning as needed, until golden, about 2 minutes. Drain on paper towels and season with salt.
Stir the remaining flour into the remaining cornmeal mixture. Dip the shrimp in the eggs, then dredge in the flour-cornmeal mixture, turning to coat. Fry the shrimp in batches, turning occasionally, until golden, about 3 minutes. Drain on paper towels and season with salt.
Season the tomatoes with salt. Serve the shrimp and okra with tartar sauce, lemon wedges and the tomatoes.