What can an observation of the lymphatic system tell the first aider about the condition of the victim?

There is no practical information that a "first aider" can derive from examination of the patient's lymphatic system. That is totally outside the scope of first aid.

i don't think this is the right system your asking about, the circulatory or respiratory system are the most important a first aider should be concerned with. feeling lymph nodes to see if there swollen to indicate if they have an infection and such is something non first aid.