Sorry I missed your reply last night. I waited for about an hour and then went to bed about 10:30.
As you probably know, lymphocytes and neutrophils are two of the 5 types of white blood cells. Since the sum of percentages of all types must add up to 100%, when one is low, others are going to be high. For that reason, percentages alone don't tell much at all. You have to examine them in conjunction with the absolute number. For example, you not that in your lab the reference range for lymphocyte percentage is 44% on the high side. All by itself, that doesn't mean much. Absolute numbers over 10,000 lymphocytes/mm³ is considered high and might have more meaning.
High lymphocytes generally mean the person has (or has recently had) an infection (even a cold or flu as well as any kind of bacterial infection), but it can also mean certain types of autoimmune disorders and also certain types of cancer (such as leukemia).
Low neutrophil percentages can also be caused by a huge number of things including leukemia, alcohol use, vitamin deficiencies, and even medications that destroy neutrophils - such as antibiotics.
All by themselves, these two percentages don't shed any additional light on the subject.
Please let me know if I can help with any additional information,