The plasticity of performance traits can promote the success of biological invasions and therefore, precisely estimating trait reaction norms can help to predict the establishment and persistence of introduced species in novel habitats. Most studies focus only on a reduced set of traits and rarely include trait variability that may be vital to predicting establishment success. Here, using a split-brood full-sib design, we acclimated the globally invasive ladybird Harmonia axyridis and a native co-occurring and competing species Cheilomenes lunata to cold, medium and warm temperature regimes, and measured critical thermal limits, life-history traits, and starvation resistance. We used the conceptual framework of “Jack, Master or both” to test predictions regarding performance differences of these two species. The native C. lunata had a higher thermal plasticity of starvation resistance and a higher upper thermal tolerance than H. axyridis. By contrast, H. axyridis had a higher performance than C. lunata for preoviposition period, fecundity and adult emergence from pupae. We combined trait responses, transport duration and propagule pressure to predict the size of the populations established in a novel site following cold, medium and warm scenarios. Although C. lunata initially had a higher performance than the invasive species during transport, more individuals of H. axyridis survived in all simulated environments due to the combined life-history responses, and in particular, higher fecundity. Despite an increased starvation mortality in the warm scenario, given a sufficient propagule size, H. axyridis successfully established. This study underscores how the combination and plasticity of multiple performance traits can strongly influence establishment potential of species introduced into novel environments.