Put the chicken tenders in a large bowl and cover with the buttermilk. Stir in the hot sauce. Set aside to marinate for 10 minutes to 1 hour.
In a nonreactive medium skillet, heat the olive oil over moderately low heat. Add the garlic and cook until softened, about 4 minutes. Add the jalapeños, increase the heat to moderately high and cook until the chiles wilt, about 2 minutes. Add the tomatoes and boil, stirring often, until the sauce thickens, about 5 minutes. Season with salt.
Heat a large cast-iron skillet over moderate heat for about 5 minutes. Add 1 tablespoon of the vegetable oil and increase the heat to moderately high. Add half of the okra and fry, shaking the pan, until the okra is bright green and just tender, about 4 minutes. Transfer the okra to a plate. Add another 1/2 tablespoon of oil to the pan and fry the remaining okra. Season with salt.
Put the cornmeal on a large, shallow plate. Remove the chicken from the buttermilk and shake lightly. Season the tenders with salt and dredge them in the cornmeal.
In the same cast-iron skillet, melt 1 tablespoon of the butter in 2 more tablespoons vegetable oil over moderately high heat. Add the chicken tenders to the skillet without crowding and fry until lightly browned and crisp, about 3 minutes per side. Adjust the heat if the oil gets too hot. Drain the chicken on paper towels and fry the rest, using the remaining 1/2 tablespoon vegetable oil and 1 tablespoon butter.
Meanwhile, reheat the tomato sauce. Spoon the sauce onto plates and arrange the chicken and okra beside it. Garnish with the lemon wedges or pass them separately.