Preheat the oven to 450°F and line a large rimmed baking sheet with parchment paper.
Prepare the Cilantro-Lime Mayo by combining the mayonnaise, lime juice, garlic and chopped cilantro in a mixing bowl. Transfer to a small serving bowl, add some Thai chili sauce to a second serving bowl and set both aside until ready to use.
Quarter each tilapia fillet lengthwise, then cut crosswise into 3-inch long pieces.
Beat the eggs and milk together in a shallow dish (a pie plate works well).
Combine the panko, lime zest, salt, a few grinds of black pepper and the oil in a separate shallow dish. Use your fingers to combine thoroughly so the oil is distributed evenly through the crumbs.
Dip each piece of tilapia in the egg mixture, allow the excess to drain off, then roll in the panko mixture, pressing gently to make sure the crumbs adhere.
As you work, transfer the fish sticks to the baking sheet leaving about an inch of space between them.
Bake the fish for 15 to 18 minutes, or until the crumbs are crisp and golden and the fish flakes easily.
Serve immediately, passing the dipping sauces at the table.