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?
Diamonds melt fairly easily, but I find it hard to believe there are huge lakes of melted diamonds well down in the mantle...
Carbon such as graphite or coal when heated and pressurized makes artificial diamonds(zircons)!
Badly written article.
According to this https://www.sciencedaily.com/releases/2017/02/170213090756.htm it is “Under the western US is a huge underground partially-molten reservoir of liquid carbonate. It is a result of one of the tectonic plates of the Pacific Ocean forced underneath the western USA, undergoing partial melting thanks to gasses like CO2 and H2O contained in the minerals dissolved in it.”