The ascent and advance of volcanic dome lava is non-linear and viscoelastic. There exists a mismatch between current theoretical approaches to dome lava rheology, which are based on rheological laws for viscous suspensions, and empirical experimental approaches to convolved viscous-brittle deformation, which show mixed evidence for simultaneous lava flow and fracturing. The missing requirement is a unified framework for understanding the transition between micro-mechanical flow mechanisms that are dominantly viscous, and those that include micro-cracking in multiphase suspensions such as magmas. Here, we use high-temperature compression rheology with sample-scale acoustic emission analysis to constrain the conditions under which crystal-rich volcanic dome lava can flow by mixed viscous and brittle fracturing processes at small scales, leading to ‘crackling’ acoustic signals, even at moderate shear stresses extant in nature. Using multi-directional permeability measurements on large 60 mm diameter quenched samples of natural magmas, we show that this micro-cracking flow mechanism leads to permeability anisotropy, localizing outgassing into pathways that are off-axis relative to the direction of flow. Finally, we use a scaling approach and a database of published observations from real eruptions to upscale our findings, and show that bulk, apparently ductile flow of low-porosity dome magma is likely to involve a local mixed-mode of micro-cracking and viscous flow during the shallowest portions of ascent and during emplacement on the Earth's surface. The micro-cracking involved in lava advance divorces real crystal-bearing lava emplacement from most current rheology models based on a purely viscous micro-mechanism and shows that a revised solution for the rheology of mixed brittle-viscous flow is required. By re-examining published numerical models for dome emplacement, we demonstrate that the viscous-brittle transition can be intercepted in spatially heterogeneous zones within the dome core.