In recent years, there has been extensive research into the development of cheaper and more sustainable carbon fiber (CF) precursors, and air-gap-spun cellulose-lignin precursors have gained considerable attention where ionic liquids have been used for the co-dissolution of cellulose and lignin. However, ionic liquids are expensive and difficult to recycle. In the present work, an aqueous solvent system, cold alkali, was used to prepare cellulose-lignin CF precursors by wet spinning solutions containing co-dissolved dissolving-grade kraft pulp and softwood kraft lignin. Precursors containing up to 30 wt% lignin were successfully spun using two different coagulation bath compositions, where one of them introduced a flame retardant into the precursor to increase the CF conversion yield. The precursors were converted to CFs via batchwise and continuous conversion. The precursor and conversion conditions had a significant effect on the conversion yield (12–44 wt%), the Young’s modulus (33–77 GPa), and the tensile strength (0.48–1.17 GPa), while the precursor morphology was preserved. Structural characterization of the precursors and CFs showed that a more oriented and crystalline precursor gave a more ordered CF structure with higher tensile properties. The continuous conversion trials highlighted the importance of tension control to increase the mechanical properties of the CFs.