How dangerous is a supurating skin lesion?

It depends... On the cause! both infectious and inflammatory conditions cause these. Talk to your primary care doctor or dermatologist to determine what you have, then you will be better able to know how to treat it!
Suppurating lesions. Suppurating lesions of the skin usually means an infection with strep or staph occasionally pseudomonas maybe the cause. All these organisms require aggressive treatment. See your doctor immediately, get a culture and sensitivity for the proper antibiotic treatment.
Depends. Need more description of the lesion and the area in which the lesion is present and the underlying illnesses the patient may have. If it is a diabetic foot ulcer it may be life-threatening. If it is a staphylococcal boil it may be very simple to deal with.