Multi-objective optimisation coupled with building energy simulation (BES) and life cycle assessment (LCA) models is a promising method to eco-design net-zero energy buildings (NZEBs) in line with sustainable objectives such as UN SDG's goals 7, 11, 12 and 13. This paper presents a method of building multi-objective optimisation based on NSGA-II coupled with the BES model COMFIE and the building LCA tool EQUER to identify NZEB designs that minimise construction costs and GHG emissions. A dynamic electricity mix model was implemented in LCA to evaluate more precisely time-related impacts of heating and solar photovoltaic production. Three different LCA approaches defining the multi-objective optimisation problem were compared: static LCA (considering an average annual electricity mix), dynamic attributionnal LCA (average hourly mix) and dynamic consequential LCA (marginal hourly mix). Results show minor differences in optimums quality between static and dynamic attributionnal approaches but important differences in optimums design parameters between attributionnal and consequential approaches. The influence of the LCA approach on multi-objective optimisation results emphasises the need to specify guidelines for practitioners about the choice of the LCA approach.