I don't know exactly but maybe it means that for every person who is lost, within themselves lies the potential for a miracle. Bones are the foundation or structure upon which human bodies are built so maybe He means that within each person lies the foundation or the structure onto which that lost person can build miracles. It's tricky to understand even for a native speaker. The beauty of song lyrics is that you can interpret them in any way you want. :)

I think that this sentence is an example of omitting words, for poetic purposes, as follows: “In every lost soul [there exist] the bones of a miracle.” I think that Shaun’s explanation of what “bones of a miracle” means is correct.