Parental influences on offspring phenotype occurring through pathways other than via inherited DNA sequences are known as parental effects. Parental effects profoundly influence offspring behaviour, including behaviour laterality and personality, two traits that are widespread and of fundamental importance in the animal kingdom with clear fitness consequences. However, the impact of parental effects on the interaction between behavioural laterality and personality within the same species has not been previously explored. If such a link exists, it would deepen our understanding of personality traits, extending them to brain laterality and its underlying neurobiology. In addition, if both traits are causally linked, it may constrain evolution as changing one of these traits would affect the other. The aim of this study was to examine whether offspring personality traits and behavioural laterality are related and can simultaneously be influenced by parental effects, suggesting a common underlying mechanism. Here we exposed parents of an egg-laying species, the stickleback Gasterosteus aculeatus, to a predator cue or not and examined the impact of this exposure on two behavioural traits of their offspring. Shortly after laying, clutches were split: half were reared without predator cues for 12 weeks before behavioural testing, and the other half were used for cortisol analysis. We found that both parents and offspring from predator-exposed parents were bolder, with the offspring more likely to show lateralized behaviour, and were smaller than offspring from parents that were not exposed to predation. The egg cortisol levels were too low to be detected by LC-MS/MS. To our knowledge, these results are the first to indicate that parental effects under varying predation conditions can influence laterality, personality and growth of offspring within the same individuals, although further evaluation and experiments are needed to determine the role of maternal cortisol.