Additive manufacturing enables the fabrication of periodic ceramic lattices with controllable micro-architectures. Many studies reported their catastrophic brittle fracture behaviour. However, ceramic lattices may fail by a layer-by-layer pseudo-ductile fracture mode, by controlling micro-architectures and porosities. Moreover, their fracture behaviour can be optimised by introducing strut/wall thickness gradients. This paper investigates the fracture behaviour and the fracture mode transition of ceramic triply periodic minimal surface (TPMS) structures. Alumina TPMS structures with relative densities of 0.14-0.37 are fabricated by ceramic stereolithography. Quasi-static compression tests validate a transition density range for non-graded samples: low (<0.21) and moderate (>0.25) relative density samples show layer-by-layer pseudo-ductile and catastrophic brittle fracture modes, respectively. The pseudo-ductile failure mode increases the energy absorption performance, enabling load-bearing capacity for a compressive strain up to 50%. With appropriate thickness gradients, graded structures exhibit significant increase of energy absorption without a decrease of fracture strength compared to their non-graded counterparts.