Wine lee generation, a by-product of the wine industry, implies economic challenges for producers in terms of management due to its high organic load and low pH value. Biological treatment based on controlled anaerobic digestion may emerge as a viable management alternative given its promising potential for biogas production thanks to the organic content of the substrate. However, the complex properties of wine lees may lead to microbial activity inhibition and process kinetics failure. Various solutions have already been explored, including co-digestion with other substrates, or the application of different pretreatments, to mitigate the effects of the accumulation of phenolic compounds, volatile fatty acids, antioxidants, or the acidic pH value of the medium. In this study, laboratory-scale batch reactors were established, adding iron- (magnetite) or carbon (graphite)-based microparticles to assess their impact on the kinetics of the process. The results demonstrate a significant improvement of 35% in the potential production of biomethane after four days of operation with graphite particles and 42% after five days using magnetite particles. Methane production rates, as determined by the Gompertz model, were 45.38 and 46.54 mL CH4∙gVS−1∙d−1 for the application of graphite and magnetite microparticles to the medium, respectively, compared to the value of 33.46 mL CH4∙gVS−1∙d−1 for the control trial, confirming kinetic process improvements of 36% and 39%, respectively. Evidences of the acceleration of the methanogenesis phase were detected along the essays; however, the strong inhibition mediated by the carboxylate accumulation was not avoided in any of the tested conditions.