Heat oil in Dutch oven or deep 12-inch skillet over medium heat until hot. Brown brisket evenly. Remove brisket; pour off drippings.
Add onions to Dutch oven; cook and stir 5 minutes or until tender. Return brisket to Dutch oven. Add water, bring to a boil. Reduce heat; cover tightly and simmer 2 hours.
Add carrots, brown sugar, lemon juice, salt, cinnamon, and pepper; continue cooking covered, 30 minutes or until meat is fork-tender. Remove brisket and carrots; keep warm.
Add prunes to Dutch oven; cook uncovered over medium-high heat 5 minutes, or until liquid is reduced to 1 cup and prunes are plumped.
Trim fat from brisket; carve diagonally across the grain into thin slices. Serve with carrots, prunes and sauce.