To prepare tartar sauce, combine first 6 ingredients, stirring with a whisk. Let stand 10 minutes.
To prepare crab cakes, place bread in a food processor; pulse 10 times or until coarse crumbs measure 2 cups. Combine 1 cup breadcrumbs, onion, and next 8 ingredients (through egg white); mix well. Divide crab mixture into 8 equal portions. Form each portion into a 1/2-inch-thick patty. Place 1 cup breadcrumbs in a shallow dish. Dredge patties, one at a time, in breadcrumbs.
Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 4 patties; cook 3 minutes on each side or until golden brown. Repeat procedure with remaining oil and patties. Serve with tartar sauce. Garnish with parsley sprigs and lemon wedges, if desired.
Tip: The tartar sauce stands for 10 minutes to let the flavors meld, but you can make it up to a day ahead and store it, covered, in the refrigerator. Lump crabmeat makes great crab cakes, but they're prone to falling apart. Handle them patiently and gently for the best results.