How to Make It
In a small bowl, combine the olive oil with the lemon juice. Season the dressing with salt and pepper. On one half of a serving platter, season the onion and tomato slices with salt and pepper and add the parsley. Spoon 2 tablespoons of the lemon dressing on top and toss lightly.
Season the liver slices with salt and pepper. In a large nonstick skillet, heat the vegetable oil until shimmering. Add the liver and cook over high heat until browned, about 2 minutes. Reduce the heat to moderate and continue cooking for 1 minute longer. Turn the liver slices and cook until rosy in the center, about 3 minutes longer. Transfer the liver to the platter with the tomato salad and drizzle with the remaining lemon dressing. Sprinkle the liver with the chopped thyme and minced chile and serve right away.