Hello! What does your lung doc say? You really need to get a doctor's input, because they are familiar with your condition, your prescriptions, and what might cause more harm than good.
When my dad had his lung cancer, non-small-cell, they didn't want him to use anything when he had a really productive cough. Other times, he used over-the-counter liquid Robitussin DM -dextromethorphan- (cough suppressant) and cough drops to find relief. It did help quite a bit. It will not work for some coughs. It's really important to get the okay of a doctor though, before you throw new medications into the mix, because you have a lot going on with both lungs.
A cough that doesn't go away is a symptom of lung cancer.