Boil the cuttlefish in a medium pot of water for about 10 minutes, or until fork tender. Drain and cut into thin strips and toss into a large bowl.
For the celery: use a vegetable peeler to create thin shavings. (To make the shavings crispier, chill them on a bed of ice for a few minutes.)
Add the celery shavings to the bowl along with the walnuts, freshly squeezed lemon juice, extra virgin olive oil, and salt. Mix well.