Cloud storage would work for all new photos you add and they would sync to any device and computer. I’m not sure about your existing photos. Maybe if you set up an in-app subscription on the old phone everything would upload to the cloud. Someone else may know for sure.
What you can do to transfer the free Lr version with your photos/data to a new phone, is to restore your new phone from a recent iOS backup which you have created from your previous phone. Hope this helps. But of course the safest way is to sync to the Lr Cloud. Hope this helps - Guido/ Lr Mobile QE