I'm sorry to hear of this with your LabX. I'm concerned that his nonsteroidal antiinflammatory drug (NSAID) + narcotic hasn't prevented "break through" pain although there are many considerations other than pain when such panting is seen.
Excessive panting can represent both medical and behavioral problems. It's often seen with elevated ambient temperature, exercise, anxiety, or perceived pain. To confound the diagnosis further, it's also seen with fever, narcotic administration, glucocorticosteroid (prednisone, e.g.) therapy, Cushing's disease, hyperthyroidism, hypocalcemia, pheocromocytoma (an adrenal gland tumor), cardiac disease, tachyarrhythmias (fast irregular heart rates), brain disease and obesity.
His vet needs to know what you're currently seeing. A recheck physical exam including diagnostics in the form of blood and urine tests should be considered. Further diagnostics such as X-rays or ultrasound should be predicated on the findings in his exam. Please let me know if you're seeing any other untoward symptoms or you have additional questions or concerns.