Despite numerous experimental investigations our understanding of atomic structure and electrochemical behaviour of SiOCs is still limited. In this contribution, density functional theory (DFT) calculations are used to model lithiation of SiOC from a an atomistic and electronic perspective. We first address the challenge of designing realistic structure models. For pristine SiOC, the lack of the existence of a crystalline phase prevents straightforward structure-generation using a cook-and-quench approach. In recent literature, SiOC models that were obtained by replacing O by C in amorphous SiO2 networks have been presented. However, such models suffer from the fact that O is only 2-fold coordinated in SiO2, while C prefers a 4-fold coordination in the vicinity of Si. Therefore, the carbon in such SiOC models is expected to be more reactive than in reality. We present a strategy that results in model structures that consist of Si and C that are mainly 4-fold coordinated while O is 2-fold coordinated. In addition, a free carbon phase is included in our models. After structural optimization and thermodynamic characterization, we study Li insertion. In particular we present information about Li storage sites, energetic evolution (including voltage profiles), structural evolution (including specific volume changes) and elastic properties. We compare our results to experiment and previous modelling studies.