Check the smoked mackerel fillet for any remaining small bones and remove them. Shred the fish with two forks into fine pieces and place in a bowl. Rinse the celery, trim the ends, and slice the stalks into very thin slices. Clean the green onions, remove the root end and the dark green part, and slice the rest into thin rings.
Add the sliced celery and green onions to the bowl with the mackerel. Then add the mayonnaise and fresh lemon juice. Toss everything together until all ingredients are evenly mixed.
Season the mackerel salad with salt and freshly ground black pepper. Cover the bowl and refrigerate for fifteen minutes to let the flavors blend.
Remove the salad from the refrigerator and serve immediately. Use the mackerel salad on toasted bread, on a cracker, or as a filling for a wrap.