The generalized lagging behavior in solids under high-rate heating is derived by precise correlation with the hyperbolic two-step model. The ballistic behavior of heat transport in the electron gas is found to be captured by the second-order effect of the phase lag of the heat flux vector. In contrast to the parabolic two-step model, the ballistic behavior results in a sharp wavefront in the history of heal propagation. The analytical expression for the thermal wave speed is derived. In comparison with the classical diffusion and the wave models, the two phase lags in the lagging response result in a much deeper thermal penetration depth and much higher temperature in the heat-affected zone.