This article is for an older version of CCC. You can find the latest version here.

FileVault protects the contents of your home directory by enclosing it in an encrypted disk image. When you log in, the encrypted disk image is unlocked via your login and password and mounted for use as your home directory. Mounted disk images pose an interesting problem to incremental backup utilities. By simply being mounted and accessed (e.g. via browsing the contents), the content of a disk image, and thus the disk image file itself, is modified. If you run CCC while logged in to a FileVault-protected account or while a read/write disk image is mounted, there is a strong chance that the disk image will be modified while it is being backed up, resulting in a corrupted version of the disk image on your backup volume. Also, because the contents of your FileVault-protected home directory are technically on another volume, CCC will not back up the contents of your home directory when backing up your root filesystem (e.g. your boot drive).

For these reasons, you should either exclude your FileVault disk image file from your backup routine while logged into a FileVault-protected account (and set up a separate routine for backing up the contents of your home directory), or you should only run CCC while logged into an account that is not protected by FileVault. Likewise, if you have other very large files (e.g. Parallels or VMWare container files) that are frequently modified, you should either quit the applications that modify those files for the duration of the backup, or you should set up a separate task for backing up those files when they are not typically in use.

"Are special steps required to back up a volume protected by Lion's FileVault 2?"

No, FileVault 2 works completely differently. Rather than placing your files into a disk image, the entire volume is encrypted. CCC can back up to and from FileVault 2 encrypted volumes just fine without any additional steps. If you would like to enable encryption on the backup volume, see the Full Disk Encryption (Lion only) section of the documentation.