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Migrate to Amazon Aurora:

Amazon Aurora is a MySQL-compatible, high-performance database designed to provide higher throughput than standard MySQL. Migrating the database to Aurora will enhance the performance and scalability of the database, especially under heavy workloads.

Add Aurora Replica:

Aurora Replicas provide read scalability and improve availability. Adding an Aurora Replica allows read operations to be distributed, thereby reducing the load on the primary instance and improving response times during peak periods.

Configure Amazon RDS Proxy:

Amazon RDS Proxy acts as an intermediary between the application and the Aurora database, managing connection pools efficiently. RDS Proxy reduces the overhead ofopening and closing database connections, thus maintaining fewer active connections to the database and handling surges in database connections from the Lambda functions more effectively.

This configuration reduces the database's resource usage and improves its ability to handle high volumes of concurrent connections.

References

AWS Database Blog on RDS Proxy​(Amazon Web Services, Inc.)​.

AWS Compute Blog on Using RDS Proxy with Lambda​(Amazon Web Services, Inc.)​.