Heat oil in heavy large pot on the grates of the grill. Add the onion and cook until soft. Add the garlic, fennel seeds, crushed red pepper and salt and cook for 1 minute.
Add wine, lemon slices, and 1/4 cup parsley; bring to boil. Add mussels. Cover pot and cook until mussel shells open, stirring once, about 6 minutes; discard any mussels that do not open. Using slotted spoon, transfer mussels to large shallow bowl. Boil broth in pot until reduced to 1 cup, about 3 minutes; season, to taste, with pepper. Pour broth over mussels. Sprinkle with tomatoes and remaining parsley.
Brush bread on both sides with oil and season with salt. Grill until golden brown on both sides. Serve mussels with bread for dipping.