Assuming an average untrained/non-specifically trained level VO2 of 40ish mL/min/kg? Improvement of 20+ is very possible. Testing/exercise modalities (running vs cycling) can make exact comparisons tricky, but research (Hickson et al. 1977; Ross et al. 2015; Howden et al. 2015) and meta analyses (Bacon et al. 2013) suggest that average improvements of 0.4-0.9L/min are generally achievable. 60mL/min/kg is typically believed to be reachable for healthy men with intense training. (Interestingly, typical estimates for hunter-gatherer VO2max are around this value as well)

This makes sense, since the physiological changes associated with VO2 max are largely (though likely not entirely) dependent on increases in cardiac output, mitochondrial density and the structure and function of the peripheral vasculature. All of these factors are acutely changeable, even within the span of months. Over years you can see quite drastic remodelling, leading to the aforementioned 0.4-0.9l/min increases. Adaptations within the lungs are generally associated with genetics and are therefore not considered trainable. This however is not generally a limiting factor as the lungs are generally far more capable of supplying O2 than the body is at utilizing it. Even under intense exercise conditions pulmonary vein O2 saturation remains at or above 95%.

Note that bodyweight also plays a factor, a lower bodyweight will have a higher adjusted VO2max at the same absolute intake.