The impact of frequency dependence of soil parameters on the lightning response of grounding systems is particularly significant, especially for systems with high soil resistivity. However, incorporating this behavior in the time domain can be challenging. To address this issue, various approaches in the literature have been explored and compared in this paper. Furthermore, the author has made notable enhancements to a recently developed method designed for this specific task. To validate the effectiveness of these improvements, a comprehensive comparison was conducted against alternative approaches. The study demonstrates that the developed method, which includes frequency dependence of soil parameters in time domain simulation, exhibits higher accuracy in simulating the lightning response of grounding systems. This holds true even for systems with large dimensions and strong frequency-dependent behavior, such as grounding systems with high soil resistivity exposed to fast lightning impulses. Additionally, the model also incorporates the phenomenon of soil ionization.