Line a shallow baking dish (or baking tray with a slight lip), about 30cm x 20cm in size, with baking parchment.
Pat dry the feta pieces, then dip each piece in the flour, gently shaking off the excess. Coat in the egg, followed by the sesame seeds, making sure the feta pieces are completely coated. Transfer each piece to your prepared dish and refrigerate for at least 30 minutes, or longer if time allows.
Preheat the oven to 220°C fan. Drizzle the coated feta pieces with the oil and bake from cold, for 18 minutes, very gently flipping the pieces over halfway, or until golden and warmed through.
While the feta is baking, put the honey and black lime, if using, into a small saucepan on a medium-high heat. Once it starts to bubble, turn the heat to medium and cook, stirring occasionally, until it turns a deep amber caramel, about six to seven minutes. Take off the heat and stir in the lemon juice. Set aside to cool for five minutes.
Use a small, sharp knife to peel and segment the remaining two lemons and stir the segments into the cooled honey mixture.
When ready, pour the lemon syrup directly over the feta in the baking dish, sprinkle with the thyme and serve at once, straight from the dish.