The paper investigates the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. The authors use a generalized Einstein-Maxwell-Dilaton action to construct a gravity model that includes Lifshitz cases as a special limit. They study the relationship between Lyapunov exponents and black hole phase transitions, considering both timelike and null geodesics. The discontinuous change in the Lyapunov exponent during phase transitions serves as an order parameter with a critical exponent of 1/2 near the critical point. The study reveals that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalized beyond AdS spacetime and is independent of the HSV parameter and the Lifshitz exponent. The findings provide insights into the phase structure of black holes in Lifshitz and HSV spacetimes, extending the understanding beyond AdS spacetime.The paper investigates the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. The authors use a generalized Einstein-Maxwell-Dilaton action to construct a gravity model that includes Lifshitz cases as a special limit. They study the relationship between Lyapunov exponents and black hole phase transitions, considering both timelike and null geodesics. The discontinuous change in the Lyapunov exponent during phase transitions serves as an order parameter with a critical exponent of 1/2 near the critical point. The study reveals that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalized beyond AdS spacetime and is independent of the HSV parameter and the Lifshitz exponent. The findings provide insights into the phase structure of black holes in Lifshitz and HSV spacetimes, extending the understanding beyond AdS spacetime.