Fragility functions are vital tools in volcanic risk assessments to evaluate the probability of damage to structures at given hazard intensities. Traditionally, lava flow damage is assumed to be binary, whereby in contact with lava results in complete destruction and not in contact with lava remains undamaged. However, past studies present examples of structures exhibiting resistance to lava and not destruction. Developing empirical fragility functions requires damage data. We collected data from field campaigns and aerial imagery to assess damage across three case studies: 2021 Cumbre Vieja lava flows, La Palma, 2018 lower East Rift Zone lava flows, Kīlauea, Hawaiʻi, and 2014–2015 Fogo lava flows, Cabo Verde. This involved manually digitising 4545 structure footprints and assigning types and damage state categories to 10,439 structures. Of the impacted structures, 6 % were classified as damaged (not destroyed). Using this dataset, we developed the first empirical fragility functions from multiple eruptions for assessing lava flow damage, for masonry, metal, and timber building types. The functions reflect the probability of a structure sustaining any of six levels of damage severity given final lava flow thickness. Lava flows thicker than 6 m generally destroy structures, but some structures, particularly masonry buildings or those with a circular shape, can resist flows thinner than 6 m. The fragility functions reflect that lava flow impacts are not binary, and that structure types and shape are important. These empirical fragility functions can differentiate between structural attributes, thereby enhancing damage, risk, and impact assessments for lava flows, for places with similar building types.