Diabetic Ketoacidosis (DKA): The presence of ketone bodies (6.4), anion gap (21), low carbon dioxide (8), and low glucose (61) are indicative of DKA, a serious complication of diabetes. The patient's lethargy and anorexia also support this diagnosis.

Inborn Errors of Metabolism: The patient's age, lethargy, and anorexia, combined with the abnormal lab results (elevated anion gap, ketone bodies), could suggest an inborn error of metabolism, such as organic acidemia or fatty acid oxidation disorder.
Infectious Gastroenteritis: Although the patient does not have nausea, vomiting, or fever, infectious gastroenteritis could still be a consideration, especially if the patient has been exposed to a viral or bacterial pathogen.

Septic Shock: Although the patient's vitals are within normal limits, septic shock can present with non-specific symptoms, such as lethargy and anorexia, especially in young children. It is crucial to consider this diagnosis to avoid missing a life-threatening condition.
Meningitis or Encephalitis: The patient's lethargy and anorexia could be indicative of central nervous system infection, which requires prompt diagnosis and treatment to prevent long-term sequelae.
Intussusception: This condition can present with non-specific symptoms, such as lethargy and anorexia, and can lead to severe complications if not diagnosed promptly.

Reye's Syndrome: This rare condition, associated with the use of aspirin during viral infections, can present with lethargy, anorexia, and abnormal liver function tests.
Mitochondrial Disorders: These disorders can present with non-specific symptoms, such as lethargy and anorexia, and can be associated with abnormal lab results, such as elevated lactate and ketone bodies.
Congenital Adrenal Hyperplasia: This condition can present with non-specific symptoms, such as lethargy and anorexia, and can be associated with abnormal electrolyte levels and metabolic disturbances.