When the oil is hot, lower two eggplant slices into the hot oil. Lay the slices away from you, so you don't get splattered by hot oil. When the edges start looking browned, carefully flip them over using your silicone tongs and a spatula. They are big, and will want to splash, so take care. Remove to drip rack when the second side is browned sightly. Do not over-brown. They will finish cooking in the lasagna.
Note: Be very careful when frying, as the oil is extremely hot. Use your stovetop ventilation fans to keep from setting off smoke alarms (lesson learned the hard way, lol).