Final answer:
For a Type 1 diabetic patient presenting with lethargy and vomiting, the initial nursing action should be to start an intravenous infusion of normal saline to address dehydration and stabilize the patient.
Step-by-step explanation:
The action a nurse should implement first for a client with a history of Type 1 diabetes, who is lethargic and vomiting, is d. Start an intravenous infusion of normal saline.
This initial response is critical as the client may be experiencing diabetic ketoacidosis, a potentially life-threatening complication of diabetes characterized by dehydration, electrolyte imbalance, and acidosis. Administering an intravenous infusion of normal saline would help to address dehydration and assist in stabilizing the patient before further treatment. It is important not to administer insulin without knowing the patient's current blood glucose levels.
In addition, hypoglycemia due to too much insulin could exacerbate the patient's condition, and hypokalemia could occur due to insulin therapy. Therefore, it is essential to rehydrate the patient first and manage electrolyte imbalances before any additional treatments are considered.