VO2 max can be increased by training, as far as I know, though the degree to which improvements can be made varies markedly between individuals. Even those whose heart and lungs are in top shape can increase their VO2 max for specific activities. For example, were you to test my VO2 max while cycling it would be higher than if you tested it while running, because my cycling-specific muscles are better trained, and therefore likely to be more heavily vascularised, and to be able to take up more oxygen as a result.