In this paper, we investigate a joint real-time load scheduling and energy storage management at a grid-connected solar powered electric vehicle. Without any a priori knowledge, we consider a finite time approach with arbitrary dynamics of system inputs. Our aim is to minimize an average aggregated system cost through joint optimization of electric vehicle's energy procurement price, load scheduling delays, photovoltaic sufficiency in terms of locally generated renewable energy mix, and battery degradation. Through subsequent modification and reformulation of the joint optimization problem, we utilize the concept of one-slot look-ahead queue stability to solve the problem by employing the Lyapunov optimization technique. We show that the joint optimization problem is separable into sub-problems, which are sequentially solved with asymptotic optimality and a bounded performance guarantee. Simulations are carried in different scenarios and under varying weather conditions. Results show that our proposed algorithm can achieve a daily electric vehicle's photovoltaic sufficiency up to 50.50%, a monthly bill reduction up to 72.61%, and a yearly reduced CO $_2$ emission level up to 6.06 kg, while meeting electric vehicle user's energy and delay requirements.