Data is synced between Lever and TalentWall in the following ways:
Web hooks: Data synced through web hooks are in near real-time. You can find which actions have web hooks here if you're a Lever admin: https://hire.lever.co/settings/integrations
Updates: We run a progressive update every 5 minutes that should get all updates and additions but not things that are deleted. Changes to tags, departments, user permissions, and every other entity will get synced with these updates. Any failures with web hooks would also be caught up with these updates.
Imports: Deletions of all entities are only caught by a full import. Please note that imports are automatically run every evening, Pacific Time.