This study investigated the application of a conductive material, granular activated carbon (GAC), as an approach to improve anaerobic lipid degradation and methane production. Anaerobic biomethane potential (BMP) assays were performed in 120 ml batch anaerobic digestion (AD) vials using 5 gVS/L anaerobic sludge as inoculum. Different BMP assays were carried out testing the impact of increasing GAC concentrations (0-33 g/L), use of different sludge types (granular vs. crushed), different substrates (oleate C18:1, butter and dairy wastewaters) and different temperatures (15, 37 and 55 degrees C). Experimental results and model fitting showed that addition of GAC supports faster methane production, i.e. the lag-phase decreased by 2-1000% depending on the GAC concentration and AD temperature. GAC addition also showed faster consumption of both volatile fatty acid and long-chain fatty acid, particularly palmitate (C16:0). Thermodynamic modelling suggested that GAC-induced direct interspecies electron transfer is kinetically superior to conventional indirect hydrogen transfer during AD of oleate. However, when the GAC concentration exceeded 8.0 g/L, there was a 20-50% decrease in the maximum methane production compared to the control. Overall, GAC supplementation has a significant potential to improve the digestion of lipid-rich wastewater which benefits design of modern bioenergy systems. (C) 2021 Published by Elsevier Ltd.