Soak sweetbreads in ice water to cover for 30 minutes. Drain well, and set aside.
Combine celery, onion, lemon juice, bay leaf, peppercorns, and salt in a Dutch oven. Stir in water; bring to a boil. Reduce heat; simmer 5 minutes.
Add sweetbreads to broth; reduce heat, and simmer 30 minutes. Drain sweetbreads, discarding broth and other ingredients.
Immediately cover sweetbreads with ice water, and cool completely. Drain off water; remove and discard white membrane and tubes. Cube sweetbreads and set aside.
Sauté mushrooms in butter in a large skillet; stir in flour. Cook 1 minute, stirring constantly. Gradually add sherry and milk; cook over medium heat, stirring constantly, until thickened and bubbly. Reduce heat. Add mustard and steak sauce, blending well. Stir in sweetbreads.