Yes - if you're a Premium subscriber and use our backup system.
Make sure to turn it on in Settings and Online Backup. From there, if you identify yourself on any other phone, you can then restore your Life Cycle data to that phone.
Note that this is not the same as syncing Life Cycle data between devices. Life Cycle is intended like a journal, and as such, you use it on one phone. If you restore your Life Cycle data base from one phone to another, any other already existing Life Cycle data bases on that phone are overwritten.