As of 2015, there is no specific research that proves that the particular combination of lemon juice and baking soda fights disease. However, many studies documented with National Institutes of Health suggest that both lemon juice and baking soda have properties that promote health and fight disease, specifically cancer.
The main idea behind the research into using baking soda and lemon juice to fight cancer and other disease is that changing the Ph of the body can create an environment in which the disease cannot live or reproduce itself. Research studies have generally verified that this is correct. Lemons also contain limonoides, which are anti-carcinogenic properties.