How the Lymphatic system works. As lymph capillaries carry lymph away from the tissue spaces and towards the heart, they merge to form larger and larger vessels. These larger vessels resemble veins, but their walls are thinner and they have more one-way valves to prevent lymph from flowing backwards.ymphocytes are the primary cells that make up the Lymphatic system, being one-fourth of all white blood cells in the human body. Like all other white blood cells, they are produced in the bone marrow. Lymphocytes continuously travel through the body via tissue, blood or lymph vessels.