There is no identifiable structural system that is capable of resisting seismic loads, for example a post-and-beam structure where columns are not cantilevered and the connections between column and beam are not moment-resisting.
A structure without lateral load-resisting system is unstable when subjected to lateral loads, while a moment frame is able to resist seismic forces
None of these lateral load-resisting systems exist in a building classified as No Lateral Load-Resisting System
Ancient Greek temple Parthenon in Athens (construction completed in 432 BC) can be classified as No Lateral Load-Resisting System, because there is no moment connection between columns and beams; the photos show the temple during the structural rehabilitation in 2007 (B. McEwen)
This building is a part of the Royal Palace complex in Pnom Penh, Cambodia. Its lateral load-resisting system can be characterized as No Lateral Load-Resisting System because it doesn't have any apparent lateral bracing (C. Scawthorn)