AWS Lambda, a serverless computing service, can face challenges when interacting with other services such as databases due to its autoscaling feature. This leads to issues like connection pool exhaustion and cold start penalties. Amazon RDS Proxy is often recommended as a solution but has limitations of its own. Neon, an alternative serverless Postgres service, integrates PgBouncer directly into its architecture for efficient connection management. Pooled connections can significantly improve performance in serverless applications by allowing more concurrent requests without overloading the database.