Whizz the avocados in the small bowl of a food processor with the juice of 2 limes, half the coriander and a pinch of salt and pepper (or mash the avocado in a bowl, then stir in the other ingredients, finely chopping the coriander first).
Put the remaining lime juice and the lemon juice in a non-reactive (glass or ceramic) bowl. Season the fish with salt, then slice as thinly as you can using a sharp knife and add to the citrus juice. Leave for 10-15 minutes until the flesh is opaque.
Spread the avocado mixture evenly onto 4 serving plates, then top with slices of fish. Scatter with the sliced chilli, red onion, cucumber, cress and pomegranate seeds, then finish with a drizzle of extra-virgin olive oil and freshly ground black pepper. Serve immediately.