Please note that this recipe takes 36 hours to complete.
Begin curing the salmon the day before. Combine the salt and sugar and mix well. In a shallow nonreactive container which is large enough to accommodate the salmon fillets in a single layer, spread half the salt/sugar mixture, reserving the balance. Lay the salmon fillets on top of the mixture and use the rest of the salt/sugar mixture to completely cover the fish fillets. Cover and refrigerate for 24 hours to salt-cure.
Early the next day, microwave the limes in a small bowl to release the essential oils, and set aside until they are just cool enough to handle. Soak the salmon fillets in cold water to remove most of the salt. Rinse and dry the same non-reactive container in which you cured the salmon. Place the fillets in the container and squeeze the lime juice over, cover and refrigerate for 6 to 8 hours to allow the acids in the lime juice to chemically cure the fish.
Dice the lime cured salmon into small cubes, keeping in mind that the completed salad will resemble the texture of salsa. Add red onion, scallions, and tomato and gently fold in. Season, to taste, with black pepper and chill.
Transfer salad to serving dish and sprinkle with fresh dill.