Lymphocytes do not contain leukocyte esterase and would not produce a positive leukocytes test on the reagent strip.
Positive results should be confirmed by performing a microscopic examination of the sediment. Note that white blood cells would not be seen in the sediment if they have lysed; however, the leukocytes test on the reagent strip would still be positive because the test is based on the detection of esterase, which is still present in the urine.
