1 The spleen is the largest organ of the lymphatic system. 2  Its primary function is to filter blood of damaged cells, cellular debris, and pathogens. 3  Like the thymus, the spleen houses and aids in the maturation of lymphocytes. 4  Lymphocytes destroy pathogens and dead cells in the blood.he lymphatic system is a vascular network of tubules and ducts that collect, filter, and return lymph to blood circulation. Lymph is a clear fluid that comes from blood plasma, which exits blood vessels at capillary beds.