@maxamillian,
Here is a possible workaround: You could extract the blocks from your function into a workflow and use Run workflow from workflow resource as your loop lambda. Each workflow would be scheduled asynchronously and could run over multiple activities. However, you wouldn't be able to return a result or wait until all iterations are completed (so remove your response block from the end of this workflow). You could, instead, send your email from within the second workflow. Set your loop up to run in batch mode.
Let me know if this works for you and solves your timeout issue.