The properties of DNA that make it an effective genetic material also allow it to be ideal for programmed self-assembly. Accordingly, DNA-programmed assembly has been utilized to construct responsive DNA origami and wireframe nanoassemblies, yet the replication of these hybrid nanomaterials remains a challenge. Here we report a strategy for replicating DNA wireframe nanoassemblies using the isothermal ligase chain reaction lesion-induced DNA amplification (LIDA). In this first generation, we designed a triangle wireframe structure that can be formed in one step by ring-closing its linear analog. Introducing a small amount of the wireframe triangle to an excess of the linear analog and complementary Fragments, one of which contained a destabilizing abasic lesion, led to rapid sigmoidal self-replication of the wireframe triangle via cross-catalysis. Using the same cross-catalytic strategy we also demonstrated rapid self-replication of a hybrid wireframe triangle containing synthetic vertices as well as the self-replication of circular DNA. This work reveals the suitability of isothermal ligase chain reactions such as LIDA to self-replicate complex DNA architectures, opening the door to incorporating self-replication, a hallmark of life, into biomimetic DNA nanotechnology.