I second upgrading LFDS to 11 first, and it is fully compatible with Laserfiche Server 10.4.
From the latest Directory Server 11 Release Notes:
Directory Server 11 can be installed over existing Directory Server 10, Directory Server 9, and License Manager 8.3.1 installations.
When creating a Directory Server licensing site, you have the option of importing data from a License Manager 8 database into the new Directory Server licensing site. The import process will migrate registered application information, named users license assignments, and version 8.3.x Active Directory group synchronization rules into the Directory Server site.
Directory Server 11 requires Laserfiche Server version 10.2.1 and later or Laserfiche Server 10.1 Update 3 (KB 1013882).
Upgrading Directory Server from versions prior to 10.4.3 requires changes to STS configuration (KB 1014134).
While not explicitly stated, all other Laserfiche 10.4 applications work with Directory Server 11 as well.