“Molten carbon”???
Never heard of it. The closest thing I know about is tar, or creosote...both of them compounds.
If you try to melt carbon, it ignites. I suppose if you could heat it in the absolute absence of any other element...it might go to the liquid state.
Carbon likes to form strong bonds with other elements. I fear that the crystalline structure of granite, which is made of silicone, reacting with the molten carbon, may well form dilithium crystals.
At atmospheric pressure, carbon would go from solid to gas. It needs to be compressed (which it apparently is, under the earth’s crust) to be liquid.
If it vented, we’d get some humongous flames.
This is yet another horribly written article, with an author trying to sound knowledgeable. Carbonates such as limestone do not "melt" at normal atmospheric pressure: at high temperature limestone "decomposes" into (basically) lime (CaO) and CO2. Pushed hard enough lime will melt (around 4662 deg. F!) but this has nothing to do with molten carbon. However, carbonates can melt when at both high temperature and high pressure -- this is how marble is formed.
Carbon (as in coal) doesn't melt easily either, tho' I couldn't find much info. on what it might do under pressure. The question remains: Are there lakes of pre-marble down there? Or actual melted carbon?
Then we would be able to fuel starships.
But how do you get lithium out of carbon and silicon?