Natural diamonds contain mineral and fluid inclusions that record diamond growth conditions. Replicating the growth of inclusion-bearing diamonds in a laboratory is therefore a novel diagnostic tool to constrain the conditions of diamond formation in Earth's lithosphere. By determining the carbon isotopic fractionation during diamond growth in fluids or melts, our laboratory experiments revealed that lithospheric monocrystalline and fibrous and coated diamonds grow similarly from redox reactions at isotopic equilibrium in water and carbonate-rich fluids or melts, and not from native carbon. These new results explain why most of the lithospheric diamonds are characterized by a common carbon isotopic fingerprint, inherited from their common parent fluids and not from the mantle assemblage.