The purpose of this paper is to assess techno-economically the integration of solid-oxide electrolysis in biomass-to-methanol processes: (1) The hydrogen produced by electrolysis can be used to adjust the composition of syngas from gasification to increase the conversion of carbon in biomass, (2) the oxygen as a byproduct of electrolysis can be used in the gasifier to avoid expensive air separation units, and (3) the overall process can be thermally integrated. Two integration concepts are proposed with different sizing methods of the electrolyzer: (1) the case of full conversion of carbon in biomass, in which a large electrolyzer is driven by the electricity purchased from the grid, and (2) the case of zero power exchange, in which only part of the carbon in biomass is converted reaching self-sufficiency of electricity. The three cases including the state-of-the-art biomass-to-methanol process are investigated to identify (1) possible trade-offs between efficiency and costs, and (2) under which conditions, these concepts become economically viable. With a reference methanol production of 100 kton/year, the results show that there is an optimal design for the state-of-the-art case, which offers an efficiency of 53.3% due to steam cycles and a payback time of 4.8 years. For the integrated concepts, there are sharp trade-offs between the system efficiency and methanol production cost rate. The case of full carbon conversion can reach an energy efficiency of 64.5-66.0% but results in a longer payback time of over 11 years. The case of zero-power exchange can achieve a similar efficiency as the state-of-the-art case with a slightly increased payback time of over 5.5 years. The payback time of the full carbon conversion case can be shorter than 5 years with a reduction in stack cost and electricity price, and an increase in stack lifetime.