It is widely known that dielectric elastomer (DE) material exhibits a strongly rate-dependent hysteresis in their stress-stretch response. It is experimentally observed, however, that the hysteresis of some DE materials (e.g., silicone) behaves as practically rate-independent when operating in the sub-Hz range. Despite this fact, the investigation and modeling of rate-independent hysteretic effects in DEs has received much less attention in the literature, compared to the rate-dependent ones. In this paper, we propose a new lumped-parameter dynamic model capable of describing a stress-stretch DE hysteresis with both rate-dependent and rate-independent effects. The model is grounded on a physics-based approach, combining classic thermodynamically-consistent modeling of DE large deformations and electro-mechanical coupling with a new energy-based Maxwell-Lion description of the hysteretic process. After presenting the theory, the model is validated by means of experiments conducted on silicone-based rolled DE actuators.