GDPR-compliance of AWS Athena CloudWatch connector

We are interested in using the Athena CloudWatch connector to query log statements that can potentially contain personal data. For this we wonder if there is any cross-region data transfer going on under the hood. From what we understand, this seems to be not the case since the stack itself is deployed in a certain region and the processing of the data is done within a Lambda function deployed in this region. But we would like to make sure to comply with European data protection laws.