Fill a bowl with ice water; add half of the lemon juice and 1 tablespoon salt. Peel the celery root with a paring knife. Rinse, then cut into matchsticks. Add to the lemon water and let soak 15 minutes. Drain and pat dry.
Whisk the remaining lemon juice, the mustard, vinegar, 1 teaspoon salt and 1/4 teaspoon pepper in a bowl; gradually whisk in the olive oil, then the cream. Add the celery root and toss; cover and refrigerate until ready to serve.
Arrange the frisee and radicchio on a platter. Top with the celery root mixture.