Wash the lime in hot water, dry and finely grate the peel. Halve the lime and squeeze the juice. Wash and halve the apple and cut out the core. Dice apple very finely. Mix with lime juice, sugar, salt and pepper.
Stir in the oil.
Wash the dill, shake dry and cut finely. Rinse salmon, dab dry and chop finely. Stir the dill carefully into the apple mixture.
Season again with salt, pepper and sugar. Arrange in glasses. Garnish with lime wedges and dill as desired.