What causes neutrophils and wbc to be low while lymphs are high?

Many, many things: The list is too long to list here, and it depends on the patient's individual circumstances. In younger patients, it is usually related to some transient infection. In older adults, it needs a more dedicated work up. A trained hematologist can sort this out in 2 visits, with some standard testing, including a review of the blood under the microscope.