For a two-level atom in a lossy cavity, a scheme to manipulate the non-Markovian speedup dynamics has been pro-posed in the controllable environment (the lossy cavity field). We mainly focus on the effects of the qubit–cavity detuning? and the qubit–cavity coupling strengthκon the non-Markovian speedup evolution of an open system. By controlling the environment, i.e., tuning? andκ, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved. Furthermore, it is clearly found that increasing the coupling strengthκor detuning? in some cases can make the environmental non-Markovianity stronger and hence can lead to faster evolution of the open system.