Cook bacon in a large Dutch oven until crisp. Remove bacon, and drain on paper towels; reserve drippings in Dutch oven. Crumble bacon; set aside.
Sauté onion in reserved drippings until tender. Stir in crumbled bacon, lima beans, potatoes, carrots, and 1 teaspoon salt. Add boiling water, stirring well. Cover and simmer 1 hour.
Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in remaining salt and pepper.
Add sauce to chowder, stirring well. Heat thoroughly. (Do not boil.) Serve hot in individual soup bowls.