Hi Nathan,
This should be possible with our Event Triggers. Have you tried configuring an event trigger subscription to point to the URL of your runbook? I think you want the identity attributes changed trigger, since that can tell you when a lifecycle state has changed.
- Create a new subscription to identity attributes changed trigger: Using Event Triggers - SailPoint Identity Services
- Follow this guide to setup your runbook to start from a webhook. Get the unique URL of your runbook and use that in the configuration of your event trigger subscription: Start an Azure Automation runbook from a webhook | Microsoft Learn.