Step 1In a deep, medium bowl, combine the kosher salt, lemon zest and juice, minced thyme leaves, several grinds of black pepper and garlic to form a rub. Add the rabbit pieces to the bowl, massaging the rub all over each of the pieces. Cover the bowl with plastic wrap and refrigerate overnight, or at least several hours.
Step 2The next morning, pour the buttermilk over the pieces and gently toss to coat; the buttermilk should barely cover the rabbit; if not, add just enough to roughly cover. Cover the bowl again and refrigerate for 1 to 2 hours.
Step 3Season the flour: Place the flour in a large bag, bowl or baking dish, and season with 1 1/2 teaspoons table salt and 1 1/2 teaspoons freshly ground pepper. Taste the flour, and adjust seasoning if desired.
Step 4About 1 hour before frying, remove the bowl from the refrigerator. Remove each piece of rabbit from the buttermilk, shaking gently to remove any excess buttermilk (do not attempt to dry the pieces). Dredge each piece in the seasoned flour mixture, coating completely. Shake to remove the excess flour, and set the pieces aside on a rack to dry and warm to room temperature.
Step 5While the pieces are resting, prepare the lard: Place about 4 cups lard in a large, heavy skillet or frying pan over medium heat. Melt the lard; it should come about one-half to three-fourths inch up the side of the pan (melt additional lard if needed). When the lard is just melted, add the onion rings and continue heating the lard until the onion is caramelized and the lard is hot. Remove the onion (discard it or save for another use), and check the temperature of the lard; a thermometer should read 350 degrees.
Step 6Gently place the rabbit pieces in the hot lard, being careful not to crowd. Lower the temperature to 325 degrees and fry the pieces on each side until crisp and golden brown and the meat is firm and opaque, about 5 minutes for smaller pieces and 7 to 8 for larger. Flip the pieces over and fry on the other side until done (a thermometer inserted in the meat should read 160 degrees). Remove the pieces from the hot oil and drain, skin-side up, on crumpled paper towels. Repeat until all of the pieces are fried.
Step 7Serve the pieces hot or at room temperature.