Add the sliced fennel to a large bowl; salt the fennel and give it a squeeze of lemon to prevent oxidation. Set aside and drain any accumulated liquid before dressing.
In a small bowl, combine the olives and parsley with olive oil, lemon juice, vinegar, and fish sauce; the herbs and olives should be suspended in dressing. Stir to combine.
After draining the fennel, add the dressing and mix well to incorporate.
Salt to taste if needed; garnish with lemon zest and additional olive oil.
