Lay the eggplant slices on a sheet pan; lightly sprinkle with salt and pepper.
Mix together the olive oil, balsamic vinegar and lemon juice, and lightly brush the eggplant slices.
Heat the broiler or grill pan, or low gas grill. Grill or broil the eggplant, turning over occasionally, until eggplant is very tender, 6 to 10 minutes; do not let them burn. Cook low and slow for sweetness. Remove and reserve.
Preheat oven to 350 degrees.
On baking pan, arrange 4 of the largest eggplant rounds side by side and spread each with thin layer of pesto, then top each with largest tomato rounds. Season tomatoes with salt and pepper, and top each with about 1 tablespoon feta and a pinch of chopped basil. Continue to layer, ending with cheese.
Bake in the oven (or on the grill) until cheese begins to melt, about 3 to 4 minutes. Garnish with fresh lemons.