What you are describing are components of the CBC, or complete blood count. The results of a CBC are used, perhaps along with other testing, and with examination by clinicians to come up with a complete clinical picture.
Here is a link that summarizes most of the components and their meaning in disease and health:
A low lymphocyte level can happen with aplastic anemia, in which the bone marrow may be injured and so the production of lymphocytes is decreased. Low lymphocyte counts can also occur in AIDS, in some neurological conditions such as MS, or after the use of steroids.
A high platelet count can be the result of inflammation. High white blood cell counts usually indicate some type of infection. Low red blood cell counts are consistent with various forms of anemia.
Many things can cause a high neutrophil count, such as stress on the body, inflammation, bacterial infection, seizures, or kidney disease.
Here is a link regarding the significance of neutrophils:
However, as I said, looking at the whole clinical picture is important before the doctor or clinician makes a diagnosis, so the tests must be used along with examination and a good medical history.
I hope this is helpful to you. Please feel free to ask a follow up question if you have one.