one dictionary says it means : to die of the disease, another : to suffer from the disease. Can it mean both? If so, how should one know what is meant?
Both, thus you need context.
If one succumbs to the flu virus, one may get ill but wont die. It means fails to resist. Succumbing to cancer would be fatal.
To succumb to your desires means to indulge them, you are supposed to resist, be an upright moral citizen, and all that.