If not serving avocado fries immediately, preheat oven to 200 degrees F. Line a baking sheet with paper towels.
Place flour in a wide, shallow bowl and panko in another wide, shallow bowl. In a small bowl, whisk together eggs and water.
In a deep, medium saucepan, heat 1 inch of oil to 375 degrees F, or until a few panko bits bubble vigorously when added.
Meanwhile, halve avocados lengthwise, remove pit, and slice each half into 4 wedges. Peel away skin, and coat each slice, one by one, in flour, shaking off excess. Dip in egg wash, then panko, gently pressing breadcrumbs on sides to coat. Place avocados on large cutting board or plate.
When oil is hot, fry 3 to 4 avocado slices at a time until golden brown, about 30 seconds. Gently transfer with tongs to paper towel-lined baking sheet and sprinkle generously with salt. Place baking sheet in oven to keep warm, or serve immediately with lemon slices and salsa or other condiments, if desired. Repeat with remaining avocado slices.
The only trick is the ripeness of the avocados. Frying will not improve their flavor, so they shouldn't be too firm, but they need to be firm enough to hold together. In other words, look for ripe, but not over-ripe, avocados.