Animals often evaluate the degree of risk posed by a predator and respond accordingly. Since many predators orient their eyes towards prey while attacking, predator gaze and directness of approach could serve as conspicuous indicators of risk to prey. The ability to perceive these cues and discriminate between high and low predation risk should benefit prey species through both higher survival and decreased energy expenditure. We experimentally examined whether Indian rock lizards (Psammophilus dorsalis) can perceive these two indicators of predation risk by measuring the variation in their fleeing behaviour in response to type of gaze and approach by a human predator. Overall, we found that the gaze and approach of the predator influenced flight initiation distance, which also varied with attributes of the prey (i.e. size/sex and tail-raise behaviour). Flight initiation distance (FID) was 43% longer during direct approaches with direct gaze compared with tangential approaches with averted gaze. In further, exploratory, analyses, we found that FID was 23% shorter for adult male lizards than for female or young male (FYM) lizards. In addition, FYM lizards that showed a tail-raise display during approach had a 71% longer FID than those that did not. Our results suggest that multiple factors influence the decision to flee in animals. Further studies are needed to test the generality of these factors and to investigate the proximate mechanisms underlying flight decisions.