What if a Lambda function fails to process an SQS message within the visibility timeout of the queue?

When you use a queue as an event source mapping for a Lambda function, the Lambda service polls that queue for you. It will behave like any polling code - once a poll reads a message it becomes invisible to subsequent polls unless the visibility timeout is exceeded, then the next poll will pick it up again and another function instance will process it.

Please read this document very thoroughly if you haven't done so already, to understand the nuances of how lambda works with an SQS event source - https://docs.aws.amazon.com/lambda/latest/dg/with-sqs.html

In particular please take a look at this recommendation - "We recommend setting your queue visibility timeout to six times your function timeout, plus the value of MaximumBatchingWindowInSeconds. This allows time for your Lambda function to process each batch of events and to retry in the event of a throttling error."