Peel each plantain. Cut each plantain into 6 to 8 pieces.
Heat the oil in a large heavy skillet over medium heat until shimmering. Add 6 pieces of plantain at a time and cook, turning every 30 seconds, until just golden brown. Remove the plantains from the oil with a pair of tongs and repeat this process for the remaining plantains.
Using a tortilla press, carefully press down on each piece of semi-cooked plantain until you have a 2-to-3-inch flat disk. If you don’t have a tortilla press, simply press down on the semi-cooked plantain with a small flat bottomed plate until the plantain is a 2–to-3-inch flat disk. Fry these disks in the oil for about 45 seconds on each side, until a deeper golden color. Transfer the disks to a paper towel to drain; sprinkle with salt. Repeat with remaining plantains.
Cut each avocado in half lengthwise. Remove the pit from the avocado and discard. Remove the avocado from the skin, cut into 1⁄2-inch dice, and place in a bowl. Using a vegetable peeler, remove the skin of the mango. Using a sharp knife, slice the wide flat part of the fruit off the pit. Repeat this process for the other side of the mango. Transfer the 2 mango slices to a cutting board and cut into 1⁄2-inch pieces. Add the mango to the bowl with the avocado.
Add the lemon juice and toss to combine. Season with salt and pepper. Top each of the fried plantains with equal portions of the avocado mixture. Top each tostone with a sprinkle of the red onion, and serve immediately.