It is possible to transfer the lists from one device to another. Please note that this will overwrite any list on the second device. After the transfer the 2 devices will contain identical lists.
If your lists use Contacts (as opposed to manually typed in data), then both devices will have to share the same contacts.
To do this transfer, use is made of the dropbox backup/restore. The idea is to do a backup from one device, and then a restore to the second device.
It is always advised to run the latest version of Address labels (1.50 on Mac, 5.30 on iOS). The latest versions of AddressLabels can cope with all of the zip types. So, simply select a file, and click the Restore button. You will get a warning about how proceeding will overwrite any existing lists. If you are ok with that – hit OK and restore your list.
Sorry if the following is a bit complicated, but bear with me. The situation gets tricky if you do not have the latest version of Address Labels running on all devices. Whatever version you are running, you can restore from any of the backups that are seen in the table. However, if you are running an older version on a device, you will not see all of the backups. For example, if you are running the latest Mac version (1.50), and create a backup, the backup file will have a .z21 extension. If you are running the latest iOS version, you will see this backup in the table, and can restore from it. However, if you are running the old iOS version (5.22), it will not display backups with the .z21 extension, meaning you will be unable to transfer the Mac file to your iPad, for example.
For instructions, have a look at Backup and Restores