Electric vehicles (EVs) are considered a substitute for fossil-fueled vehicles due to rising fossil fuel prices and accompanying environmental concerns, and their use is predicted to increase dramatically shortly. However, the widespread use of EVs and their large-scale integration into the energy system will present several operational and technological hurdles. In the energy industry, an innovative solution known as the EVs smart parking lot (SPL) is introduced to handle EV charging and discharging electricity and energy supply challenges. This paper investigates social equity access and mobile charging stations (MCSs) for EVs, where the owner of MCSs is the EV parking lot. Accordingly, a new self-scheduling model for SPLs is presented in this paper that incorporates scheduling of the MCSs as temporary charging infrastructures while considering social equity access and optimizes SPL energy generation and storage schedule. The main objectives of this research are to (i) develop MCSs accessibility measures and quantify the equity impacts of MCSs locations by modeling prioritized demand based on several indices; (ii) determine the optimal set-points of SPL components (i.e., combined heat and power (CHP), photovoltaic system, electrical and heat-energy storage, and MCSs) to manage electrical peak demand and to maximize the economic benefits of SPLs. Results indicate that the proposed demand prioritization function model can meet the required EV charging demands for prioritized events, and the self-scheduling model for SPLs satisfies the charging demand of the EVs in the SPL location. Also, the social equity access to the EV charging stations is satisfied by analyzing the operation of MCSs around the prioritized demand of the prioritized events and social equity access indices.