In a small bowl, combine the mayonnaise, lime zest, 1 tsp. of the lime juice, and the wasabi paste. Season to taste with salt, pepper, and more wasabi, if you like.
In a wide, shallow bowl, lightly beat the eggs and 1 Tbs. of the soy sauce until combined. Put the panko in another wide shallow bowl.
Pat the fish fillets dry and lightly season with salt. Working with one fillet at a time, dip it in the egg mixture, letting any excess drip off, then coat with the panko, pressing the breadcrumbs onto the fish. Set each breaded fillet on a plate or tray as you finish it.
In a 10-inch nonstick skillet, heat 1/2 cup of the oil over medium heat until shimmering hot. Fry the fish, flipping once, until well browned and just cooked through, 5 to 8 minutes total. Transfer to paper towels to drain and sprinkle each fillet with a pinch of salt.
Meanwhile, in a large bowl, stir together the remaining 1 Tbs. lime juice, 1 Tbs. soy sauce, 1 Tbs. oil, the ginger, 1/4 tsp. salt, and 1/4 tsp. pepper. Add the lettuce and toss to coat.
Spread the wasabi mayonnaise on both cut sides of the buns. Put one fish fillet on the bottom of each bun, and then top with the lettuce and the bun top.