With the immune system suppressed, a sufferer might find that they feel tireder generally and that they easily become worn out.
Again, this can be the result of many other conditions ranging from depression, to food sensitivities, to apnea, to malnutrition.
One thing that can make it hard to diagnose leukemia is the fact that many of the symptoms are similar to those seen in a cold or a flu. This is certainly the case for general tiredness and lethargy.