The g factor of lithium-like carbon and oxygen is evaluated to a high accuracy. The fully relativistic approach, that is used to zeroth and first order in 1/Z, is combined with the calculations based on the nonrelativistic form of the extended Breit equation to account for the higher-order interelectronic-interaction and screened QED corrections. Corresponding calculations for heavy lithium-like ions are also discussed. Special attention is focused on a possibility to reduce the uncertainty due to nuclear effects in a specific difference of g factors of heavy H- and Li-like ions.