With a very sharp knife, trim the gray fat off the skin side of the salmon; it has a strong flavor. Slice the salmon as thinly as possible.
Make the marinade: Put the lemon juice in a small bowl. Gradually whisk in the olive oil. Season with salt and pepper.
Arrange the salmon in an oiled dish large enough to hold the slices in a single layer. Scatter the celery over the fish, then spoon the marinade over all. Cover and refrigerate until the salmon is a little more than half "cooked", which you can tell by the change in color from rosy orange to pale pink. It should take about 3 hours, depending on the thinness of the slices.
To serve, divide the salmon and celery among 6 plates, reserving the marinade. Put the sliced fennel and fronds in a bowl and drizzle with enough of the marinade to coat it lightly. Toss well and season with salt and pepper to taste. Divide the fennel among the plates. Spoon a little extra marinade over the salmon.