In a shallow bowl or pie plate, mix flour with salt and pepper. Coat each fillet, turning to coat both sides.
Place 2-3 fillets onto melted butter. Cook for 3 minutes, and carefully turn over to other side. Cook another 3 minutes; gently transfer to platter (you may cover with foil to keep warm).
Pour wine or chicken stock into skillet, and squeeze juice from the lemon half into pan (about 1/4 cup).
Add remaining butter, whisking as it melts, and add lemon slices into pan. Drizzle piccata sauce over tilapia and serve warm.