This is a general chemical process of converting carbon to different carbon compounds:

Carbon $C$ reacts with oxygen $O2$ to form carbon dioxide $CO2$ through combustion or other oxidation reactions.

Carbon dioxide $CO2$ dissolves in water $H2O$ to form carbonic acid $H2CO3$ through a reversible reaction known as hydration.

Carbonic acid $H2CO3$ reacts with lithium hydroxide $LiOH$ to form lithium carbonate $Li2CO3$ and water.

Lithium carbonate $Li2CO3$ can further react with calcium chloride $CaCl2$ to form calcium carbonate $CaCO3$ and lithium chloride $LiCl$.

Each step in this chemical process involves different reactions and compounds that are interrelated in their transformations.