Note: the following applies to version 6.40 onwards, and only if you are running Address Labels on a device with Operating System 13.0 or later.
All of the lists data are now automatically backed up to your private Cloud account. There is no longer any need to backup lists to dropbox.
It is essential that iCloud is enabled for Address Labels on your device, for this to happen.
To check that iCloud is enabled for AddressLabels, please do the following. First go to the device Settings. Tap your name (where it says Apple ID, iCloud…) and then tap iCloud. Scroll down to check that Address Labels has iCloud ON.

If you are running the app on more than one iOS device, the lists will automatically sync between them, as long as you are logged on to each device with the same Apple ID.The same applies to Mac computers i.e. if you are running Address Labels on a Mac, the lists will automatically sync between devices, again assuming you are logged on to the Mac with the same Apple ID. The other Mac(s) must also be running 2.41 (and Catalina or later) and the iOS device must be running Address Labels 6.40 (iOS 13 or later).
Please note that although this is automatic, the time taken to sync is variable. Changes might occur in a few seconds, but it could also take several minutes. If you do have lists on a different device, then when you start running Address Labels on your iPad or iPhone, please allow several minutes for the lists to appear, especially on the first time of running.
Upgrading from iOS pre-6.40 Devices
It may be that you have been running Address Labels on more than one device already, and “copying” lists between them via dropbox. This would be the case when your device(s) were running version 6.40 or previous, or the iOS was previous to 13.0. So, you might have a Christmas 2019 list on your iPhone and iPad. Although the contents might be the same, they will be treated as different lists. Once you have updated to 6.40 or later, on your iOS device, and allowed time for the syncing, you will end up with two Christmas 2019 lists, as each device will copy their list to the Cloud. At that point, you can delete the list from one of the devices.
Important Note: In this situation, delete the list from just one of the devices and allow time for this to sync to the other device. Do not delete a list on each device.
If you delete one of the lists, it will also get deleted from the second device – could happen a few seconds or a couple of minutes later. If you delete a list on each device, you risk ending up with no lists on either device!