This paper studies the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. A generalized Einstein-Maxwell-Dilaton action is employed to construct a gravity model that includes Lifshitz cases in the appropriate limit. The relationship between Lyapunov exponents and black hole phase transitions is analyzed considering both timelike and null geodesics. The black hole phase transition properties are reflected in the Lyapunov exponent, which exhibits multiple branches corresponding to distinct phases. 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 shows that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalized beyond AdS spacetime, and it is independent of the HSV parameter and the Lifshitz exponent. The paper explores the thermodynamics and critical phenomena of HSV black holes, focusing on the canonical ensemble. It finds that spherical black holes exhibit a phase transition similar to charged AdS black holes, while planar and hyperbolic black holes do not. The phase diagram for spherical black holes shows a consistent qualitative pattern for all values of θ, though it varies with z. The critical charge Q_crit is determined, and the critical temperature is calculated. The study also investigates the behavior of the Lyapunov exponent for both timelike and null geodesics, showing that it reflects the phase structure of black holes. The Lyapunov exponent is found to be closely related to the radius of unstable circular geodesics and exhibits characteristics similar to those observed in AdS spacetime. The results indicate that the Lyapunov exponent provides insights into the divergence and convergence rates of particle orbits around the equatorial plane of the black hole during phase transitions. The study concludes that the Lyapunov exponent is a useful tool for understanding the phase structure of black holes in Lifshitz and HSV spacetimes.This paper studies the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. A generalized Einstein-Maxwell-Dilaton action is employed to construct a gravity model that includes Lifshitz cases in the appropriate limit. The relationship between Lyapunov exponents and black hole phase transitions is analyzed considering both timelike and null geodesics. The black hole phase transition properties are reflected in the Lyapunov exponent, which exhibits multiple branches corresponding to distinct phases. 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 shows that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalized beyond AdS spacetime, and it is independent of the HSV parameter and the Lifshitz exponent. The paper explores the thermodynamics and critical phenomena of HSV black holes, focusing on the canonical ensemble. It finds that spherical black holes exhibit a phase transition similar to charged AdS black holes, while planar and hyperbolic black holes do not. The phase diagram for spherical black holes shows a consistent qualitative pattern for all values of θ, though it varies with z. The critical charge Q_crit is determined, and the critical temperature is calculated. The study also investigates the behavior of the Lyapunov exponent for both timelike and null geodesics, showing that it reflects the phase structure of black holes. The Lyapunov exponent is found to be closely related to the radius of unstable circular geodesics and exhibits characteristics similar to those observed in AdS spacetime. The results indicate that the Lyapunov exponent provides insights into the divergence and convergence rates of particle orbits around the equatorial plane of the black hole during phase transitions. The study concludes that the Lyapunov exponent is a useful tool for understanding the phase structure of black holes in Lifshitz and HSV spacetimes.