The global spread of the COVID-19 virus has led to difficulties in many branches of the economy, including significant effects on the urban transport industry. Thus, countries around the world have introduced different mobility policies during the pandemic. Due to government restrictions and the changed behaviors of transport users, companies providing modern urban mobility solutions were forced to introduce new business practices to their services. These practices are also apparent in the context of the electric shared mobility industry. Although many aspects and problems of electric shared mobility have been addressed in scientific research, pandemic scenarios have not been taken into account. Noticing this research gap, we aimed to update a previously developed model of factors that influence the operation of electric shared mobility by incorporating aspects related to the COVID-19 pandemic and its impact on this industry. This article aims to identify the main factors influencing the electric shared mobility industry during the COVID-19 and post-lockdown periods, together with their operation areas and the involved stakeholders. The research was carried out on the basis of expert interviews, social network analysis (SNA), and the use of the R environment. The article also presents sustainable transport management recommendations for cities and transport service operators, which can be implemented after a lockdown caused by an epidemic. The results in this paper can be used to support transport modeling and the creation of new policies, business models, and sustainable development recommendations. The contents will also be helpful to researchers worldwide in preparing literature reviews for articles related to sustainable management in the COVID-19 pandemic reality.