In an eight-quart pot, bring water, split peas, lima beans, and baking soda to a boil. (After adding baking soda, lower heat for a few seconds, as it tends to cause the water to foam and boil.) Cook for one hour and 45 minutes on medium heat, stirring occasionally. Add salt when beans are nearly tender.

In a three-quart saucepan, sauté onions in oil until golden in color. Add vegetables and sauté for 20 minutes. Combine sautéed vegetables with bean soup and cook additional 20 minutes.