Combine the onion and the juice of 2 limes in a small bowl; allow the onion to soak in the lime juice for at least 1 hour. Strain and discard the excess juice. Set the onion aside.
Grind the serrano chile peppers, the juice of 2 limes, and salt together in a food processor until no large chunks of pepper remain. Add 1 avocado and process until creamy and smooth; repeat with remaining avocados. Transfer the mixture to a serving bowl; fold the onion, cilantro, and mango into the avocado mixture. Serve at room temperature.