Results of lupus test positive. No family history so how is that possible?

Unknown cause. Many lupus patients do not have a strong family history of lupus. It appears lupus patients have a genetic predisposition for the disease and then something activates the gene for lupus. A virus or bacteria or something else in the environment could set the lupus off. We do not know the exact cause.
False positive. Unlike a blood test which definitely identifies your blood type (for example, o positive, a negative, etc.), the antinuclear antibody (ANA) is only helpful in making a diagnosis of lupus if a patient already has signs and symptoms of lupus. By itself, the ANA is often positive but no associated disease is identified.