Hemoglobin is oxygen carrying compound present in red blood cells. Hemoglobin contains iron. So, low levels of hemoglobin can cause anemia which is its major symptoms. Anemia can be fatal if not treated on time. CLL or chronic lymph node leukemia is the cancer of white blood cells. This can also cause decrease in the number of red blood cells leading to anemia and low hemoglobin levels. So, Low hemoglobin levels in your case are related with CLL.