Vitamins and minerals are not central to lung diseases. Vitamins B & C can help, as they support the immune system.
Taking calcium and then drinking water with lemon or lime is a very good idea.
Best actions are: quit smoking; eliminate all food allergies and reduce exposure to environmental toxins as best you can; reduce or eliminate dairy in your diet; learn and practice deep, relaxed natural breathing (best done with qigong or yoga); develop a healthy mildly athletic fitness routine; eliminate excess sugar, caffeine, and artificial sweeteners; keep yourself well hydrated; and do not drink icy-cold liquids.
I've done this and eliminated chronic sinus infections that plagued me when I was younger. I've had very health lungs and respiratory system for the last several years.