Magma crystallisation is a fundamental process driving eruptions and controlling the style of volcanic activity. Crystal nucleation delay, heterogeneous and homogeneous nucleation and crystal growth are all time-dependent processes, however, there is a paucity of real-time experimental data on crystal nucleation and growth kinetics, particularly at the beginning of crystallisation when conditions are far from equilibrium. Here, we reveal the first in situ 3D time-dependent observations of crystal nucleation and growth kinetics in a natural magma, reproducing the crystallisation occurring in real-time during a lava flow, by combining a bespoke high-temperature environmental cell with fast synchrotron X-ray microtomography. We find that both crystal nucleation and growth occur in pulses, with the first crystallisation wave producing a relatively low volume fraction of crystals and hence negligible influence on magma viscosity. This result explains why some lava flows cover kilometres in a few hours from eruption inception, highlighting the hazard posed by fast-moving lava flows. We use our observations to quantify disequilibrium crystallisation in basaltic magmas using an empirical model. Our results demonstrate the potential of in situ 3D time-dependent experiments and have fundamental implications for the rheological evolution of basaltic lava flows, aiding flow modelling, eruption forecasting and hazard management.