For the relish: Combine the tomatillos, onions, lime juice, cilantro and oil in a bowl. Let sit at room temperature for 30 minutes. Stir in the bacon just before serving.
For the mayo: Whisk the mayonnaise and goat cheese together in a bowl until well combined. Season with pepper.
For the fried green tomatoes: Set a cooling rack over a baking sheet. Season the green tomatoes on both sides with salt and pepper. Put the flour, eggs and cornmeal in separate shallow dishes. Season all three with salt and pepper, and the eggs with the hot sauce.
Heat a few inches of oil in a cast-iron skillet over medium heat until beginning to shimmer (drop in a few grains of cornmeal -- they should sizzle) or a deep-frying thermometer registers 350 degrees F. Dredge the green tomatoes in the flour, tap off the excess, then dip in the egg wash. Let the excess drip off, then dredge in the cornmeal.
Fry the green tomatoes in batches until golden brown on both sides, 1 to 2 minutes per side. Drain on the prepared rack and season with a bit more salt.
Spread a teaspoon of goat cheese mayo on the top and bottom buns. Place a fried green tomato on the bottom buns, top with relish and serve.