Final answer:
The nurse should report behavioral changes, serum sodium level of 117, and severe headache with vomiting to the healthcare provider, as these findings are concerning in a patient with SIADH.
Step-by-step explanation:
A nurse is caring for a client who has lung cancer and is exhibiting signs of Syndrome of Inappropriate Antidiuretic Hormone secretion (SIADH). The abnormalities to report to the provider include: behavioral changes, a serum sodium level of 117, and a severe headache with vomiting. While a urine specific gravity of 1.020 indicates normal kidney function and a urine output of 50 mL per hour is within the normal range, low serum sodium levels, behavioral changes, and severe headaches with vomiting are concerning and may indicate worsening of SIADH or complications such as cerebral edema.