We need to address the delays in real-time data processing by considering several key factors. 

First, we should investigate any data failures. If numerous messages are failing and being sent to the Dead Letter Queue (DLQ), this can be quite time-consuming. It is essential to ensure that these failures are managed effectively. 

Next, we need to evaluate any external API calls or database interactions to confirm that they are functioning efficiently. By reviewing the logs, we can identify any latency issues. 

Additionally, we should consider the volume of incoming data. If the volume is excessively high, it may overwhelm the system. Increasing the number of parallel executors, whether using PySpark, Apache Beam, or Apache Flink, can facilitate faster data processing. 

Finally, we must verify the format and size of the incoming data to ensure it is appropriate and manageable. 

By identifying failures, reviewing external interactions, managing data volume, and increasing executors, we can effectively reduce the lag in real-time data processing.