Wash and dry fish filets.
Use kitchen shears to cut filets into bite-sized pieces, then place them in a large, glass container.
Slice lemons in half, then juice them with the citrus press.
Season fish pieces generously with salt, then pour lemon juice over fish until fully immersed. If needed, juice more lemons.
Allow fish to "cook" in the lemon juice for 4-8 hours, depending on whether you want your fish to taste more like sushi or more like lemon.
Dice mango and avocado into bite-sized chunks; roughly chop cilantro.
Drain fish from marinade and place in a serving dish; scatter mango, avocado, and cilantro on top of fish and serve immediately.