Final answer:
The patient's hyponatremia is most likely due to the ectopic overproduction of vasopressin by a lung mass, consistent with syndrome of inappropriate antidiuretic hormone secretion (SIADH).
Step-by-step explanation:
The most likely mechanism for the patient's hyponatremia is ectopic overproduction of vasopressin. This condition is also known as syndrome of inappropriate antidiuretic hormone secretion (SIADH). The patient's hyponatremia could be caused by a paraneoplastic syndrome, where the lung mass may be producing ADH or ADH-like substances independently, leading to water retention and dilute hyponatremia. The presented clinical features and lab values, including low plasma osmolality and relatively high urine osmolality, support this mechanism. Other options, such as increased oral intake of hypotonic fluids or decreased oral intake of solutes, are less compatible with the lab findings.