Did I get it right that you have the free version of Lightroom running on your iPhone? ...and you re-installed the app on your new phone. If so, the only way to preserve you local app data -as a free Lr user- is when you restore your new phone from an iOS back-up created from your previous phone. With that all the data should be preserved.
Even when you are signed-in as a free user a deletion of the app will delete all your local data since nothing is synced to the cloud service.