After watching my grandmother die with emphysema, I resolved never to smoke. So, when I was diagnosed with stage IV lung cancer — and told I had less than year to live — I thought, “This can’t be happening.”

I just didn’t make the connection, even though I’d had a persistent cough for a few months, been losing weight without trying, felt a heaviness in my chest and even begun coughing up blood. I thought, “How can I possibly have...