Facing the mounting pressure from the exponential growth of parcel volumes, logistics systems struggle to provide efficient, cost-effective, and reliable delivery. Mobile locker delivery is an innovative solution. However, many studies focus on parcels at the warehouse, neglecting real-time parcel arrivals during mobile locker delivery. This study addresses the real-time parcel replenishment issue in mobile locker delivery, by integrating mobile locker delivery processes with real-time parcel arrivals. The operation period is divided into multiple delivery periods. At the end of each period, a delivery plan is formulated for newly arrived parcels, covering replenishment and updated mobile locker routes. And a mixed-integer optimization model is proposed and solved by a hybrid heuristic ALNS-TS algorithm. Experimental results demonstrate that integrating mobile locker delivery processes with real-time parcel arrivals effectively reduces delivery costs, significantly enhances the capacity utilization of mobile lockers, decreases the number of lockers required, alleviates storage pressure, and improves delivery quality.