In this work, a synthesis and activation path, which enabled the preparation of spherical activated carbon from a lignin precursor, characterized by high adsorption capacity in the removal of phenolic compounds from water, was successfully developed. Two industrial by-products, i.e., Kraft lignin and sodium lignosulfonate, were used to form spherical nanometric lignin grains using pH and solvent shift methods. The obtained materials became precursors to form porous activated carbons via chemical activation (using K2CO3 or ZnCl2 as activating agents) and carbonization (in the temperature range of 600–900 °C). The thermal stabilization step at 250 °C was necessary to ensure the sphericity of the grains during high-temperature heat treatment. The study investigated the influence of the type of chemical activator used, its quantity, and the method of introduction into the lignin precursor, along with the carbonization temperature, on various characteristics including morphology (examined by scanning electron microscopy), the degree of graphitization (evaluated by powder X-ray diffraction), the porosity (assessed using low-temperature N2 adsorption), and the surface composition (analyzed with X-ray photoelectron spectroscopy) of the produced carbons. Finally, the carbon materials were tested as adsorbents for removing phenol from an aqueous solution. A conspicuous impact of microporosity and a degree of graphitization on the performance of the investigated adsorbents was found.