Step 1 Put about 1 tablespoon lemon juice in the center of each of four small serving plates and drizzle the remaining juice around the sides of the plates.
Step 2 Using a very sharp, straight knife, cut the fillet lengthwise in half, then cut each piece in half lengthwise again so that you have four long pieces. Cut away the tip ends so that the four pieces are fairly rectangular and of equal thickness. Cut each of the four pieces on the bias into slices one-fourth-inch thick, making clean, sure cuts. There should be at least 16 slices, though the size and shape of the fillets may allow for more or less.
Step 3Arrange the slices of albacore on the plates, four slices to a plate, atop the lemon juice. Sprinkle a few crunchy grains of sea salt on each slice of fish. Follow with a light grinding of black pepper on each piece and then a light drizzle of olive oil over the top. Add four caper berries to each plate and serve immediately.