If my grandma has a lung tumor/cancer, how can I support her?

Kindness. If this is treatable, or she is having only palliative care, simple kindness and willingness to help her out with chores is the best thing you can do. It's not catching; touch her. If it is smoking-related, don't remind her -- once a child becomes addicted, it is very difficult to stop. Usually this is fatal; you have a limited time to thank her for all her goodness. God bless you both.