The syn-eruptive alteration of lavas can influence their physical, mechanical, and hydraulic properties, with implications for the outgassing of magmatic volatiles and the stability of volcanic structures. Although glass corrosion, resulting in porous diktytaxitic textures, and cristobalite precipitation is a common alteration type at both submarine and subaerial volcanoes, little is known as to their impact on rock properties. Here, therefore, we provide laboratory measurements of porosity, permeability, P-wave velocity, Young's modulus, and uniaxial compressive strength for a suite of rhyolitic lavas from the 2012 eruption at Havre volcano (Kermadec volcanic arc, Pacific Ocean; sampled in 2015) that have variable textures and contain variable quantities of cristobalite. We find that the cristobalite content of the lavas varies from 0 to ~26 area%, and that the cristobalite-rich (> 10 area%) lavas are all associated with porous diktytaxitic textures. Lavas from the outermost, glassy carapace are cristobalite-poor, and lavas from the interior carapace are cristobalite-rich. Although porosity and permeability do not systematically increase with cristobalite content, the cristobalite-rich lavas from the interior carapace—those also associated with porous diktytaxitic textures—are consistently porous (> ~0.13) and permeable (> ~10−15 m2) and contain essentially no isolated porosity, which can reach up to 0.1 in the cristobalite-poor lavas from the outermost, glassy carapace. The presence of porous diktytaxitic textures in the cristobalite-rich lavas appears to lower P-wave velocity, but does not appear to reduce Young's modulus or uniaxial compressive strength. The presence of commonly-observed macrofractures in lavas from the outermost, glassy carapace increases their permeability and lowers their strength. We discuss the implications of these laboratory data for fluid movement and outgassing in, and the structure—in terms of rock physical, mechanical, and hydraulic properties—and stability of, submarine lava domes.