Your line of thinking is incomplete. There is no principle in your hypothesis from preventing such processes to occur with other compositions, be it Lithium, Iron, etc.. The Earth’s core has plenty of hydrogen - as evidenced by volcanic emissions - and plenty of iron, nickel, etc.. The geologic history of Earth is quite consistent with current conventional science. If LENR is actually occurring in Rossi’s reactor, it would occur in the Earth’s mantel and other planets and the geological behavior of planets would be quite different as what is observed today. The same applies to Rendell Mill’s hydrino hypothesis since it implies an interstellar space whose behavior would differ greatly from what we observe.
Also, there is some disagreement amongst scientists which element has the most stable isotopes: is it Iron or Nickel. More and more scientists lean toward Nickel. To go from Nickel to elements of higher atomic numbers (such as copper) is - overall - endothermic, not exothermic. The coulombic barrier between Nickel and hydrogen is greater than between, say, Sodium and hydrogen; the fusion of Na and H is exothermic and it is with Ni-H.
At best Rossi’s work would make a mild contribution to metalurgy, not LENR.
Now, do these processes take place internally?
Well, we have the THORIUM DECAY thesis where deeply buried thorium is supposed to be heating the Earth's interior.
It's just a thesis ~ with little evidence other than the finding that Earth's interior is hot.
So, why not LENR heating?
Frankly, I'm wondering if the things we see as UFOs aren't just flying LENR processes underway in bodies of gas belched out of the oceans, or volcanos, or maybe fissures.
You might look into the makeup of mantle plumes. Hot little suckers. We don't really know why they can continue being hot all the way to the top.