Use a serrated knife to peel the celery root of all the brown outer portions, like peeling a pineapple. Cut the celery root into thin matchsticks with a mandoline, or grate them in a food processor fitted with the coarsest grating blade. With the food processor, press a little as you feed the chunks through and you will have larger shreds. Place the celery root in a large bowl, sprinkle with 1 1/2 teaspoons of the salt and 2 tablespoons of lemon juice, and allow to stand at room temperature for about 30 minutes.
Meanwhile, in a small bowl whisk together the mayonnaise, the 2 mustards, the remaining tablespoon of lemon juice, the vinegar, the remaining 1/4 teaspoon of salt, and the pepper. Add enough sauce to lightly moisten the salad. (You may have some sauce left over.) Serve cold or at room temperature.