It wouldn't actually be your lung that's hurting, it's your diaphragm and intercostal muscles. you may need to learn how to breath correctly when running to help avoid the fatigue. There's actually a good answer to your question at runner's world. Here is the link:
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Posted by sewy
after jogging for like 2 mins. my lung hurts and it hurts even more if i stop... im a beginner at jogging btw...