Thick toenails are quite a common problem as people get older. Let me reassure you that your thick toenails are probably caused by a common fungal infection, not something as
serious as lung cancer. The best way to evaluate your toenail problem is to be seen by a podiatrist. They can regularly cut your toenails, which can get really difficult (and dangerous!) when they get so thick.
The good news is that the fungal infection that causes this problem in your toenails can be treated with oral medication, but it sometimes takes up to 3 months to see results. While you take this medication, you may also need lab tests while you take this medication to be sure it doesn't stress your liver.
Another reason you should see a podiatrist is because the skin problems you mention in your feet as well. You may need some kind of cream to help with that, and the podiatrist can help with that too.