Toast walnuts in a skillet over medium heat until fragrant, 3 to 4 minutes. (Do not burn!) Transfer nuts to a sieve and cool, then rub off and discard bitter skins.
Place sliced celery, fennel, sunchoke, and apple in a bowl of cold water. Stir in 1 tablespoon lemon juice and refrigerate.
In a small bowl, combine remaining lemon juice, mustard, garlic, honey, and salt. Whisk in oil and season with pepper.
Drain chilled celery, fennel, and sunchokes and dry in a salad spinner or blot with a paper towel. Combine celery, fennel, sunchokes, celery leaves, walnuts, and apples. Toss with dressing before
serving. Garnish with fennel fronds.