The effect of LPSO phases on the crack propagation in different microstructures modified by heat treatment is investigated. Solution heat treatment on a hot-extruded Mg–Dy–Nd–Zn–Zr alloy (RESOLOY) is done to change the initial fine-grained microstructure, consisting of lamellar LPSO structures within the matrix, into coarser grains of less lamellae but blocky LPSO phases. C-Ring compression tests were done with the focus on crack initiation and propagation. The blocky LPSO phases clearly hinder crack growth, either by increasing the energy to pass through the phases or along its interface. LPSO phases are found to be responsible for crack initiation: by the interface or the softer Mg-matrix in between LPSO lamellae. The softer Mg-matrix layer is providing the possibility for slip band cracking. In the coarser-grained microstructure, the crack propagation is also influenced by twins. The microstructural features were characterized by micro and nanohardness, as well as the amount and location of LPSO phases, in dependence on the heat treatment condition. Blocky LPSO phases show a higher hardness than the grains with or without lamellar LPSO phases— more specific by nanoindentation.