A process for manufacturing a part provided with a lubricating surface coating (10), in which: a composition is prepared that includes at least one precursor having at least one organic group, the composition is deposited on the part, a heat treatment is carried out, wherein the heat treatment of the coating is carried out at a temperature above 220° C., so as to form a lubricating surface coating (10) formed of an at least partially inorganic solid network incorporating solid carbon in at least one lubricating allotropic form in the dispersed state and trapped within the solid network. A part, such as a foil of a foil bearing (1) obtained by the process, a turbomachine, such as a turbomachine for a fuel cell, including such a part, and an aircraft cabin air-conditioning system including at least one such turbomachine are also described.