Setting up a DLQ offers the possibility to investigate errors or failed requests to the connected Lambda function.
As an alternative it is possible to configure an on-failure destination target, which forwards a failed event to a DLQ, SNS Topic, Lambda function or EventBridge.
It is always important to understand why your application/function failed and to ensure that no data was dropped or compromised. Lambda functions are often used to process security related data like CloudTrail events and a failed delivery to a dependent system can result in an unnoticed security breach.