A method of making a carbon fiber comprising esterification of a lignin precursor with an acid, acid anhydride, or acyl halide, thereby forming a reduced Tg lignin. Mixing the reduced Tg lignin with a carbon residue selected from the group of coal based raw material, petroleum based raw material and combinations thereof, thereby forming a fiber precursor mixture; and spinning the fiber precursor mixture into a fiber. A method of making a carbon fiber comprising esterification of a lignin with an acid derivative, thereby forming a reduced Tg lignin. Mixing the reduced Tg lignin with a pitch, thereby forming a fiber precursor mixture; and spinning the fiber precursor mixture into a fiber. A method of making a carbon fiber comprising lowering the Tg of a lignin material, thereby forming a reduced Tg lignin. Mixing the reduced Tg lignin with a carbon residue, thereby forming a fiber precursor mixture and spinning the fiber precursor mixture into a fiber.