Folders, siblings, and the permission question
Why macOS asks about the parent folder once, and what Lumeira can and cannot see.
Lumeira runs in the macOS sandbox. That is a good thing: the app can only read what you have opened or dropped in. It also means one question you will see once.
What opening a file gives the app
Open a file, or a folder, and Lumeira can read that folder. That is enough to browse every image in it, including subfolders.
What the sibling keys need
] and [ jump to the next and previous folder next to the one you are in. To know what those folders are, the app has to read the parent folder, and the sandbox has not granted that yet.
The first time you press one of these keys, or use the arrows in the folder bar at the bottom of the window, macOS shows a file dialog pointed at the parent folder. Click Open. That is the whole thing. Lumeira remembers the choice, so you will not be asked again for that parent.
If you cancel, the sibling keys stay off for that folder and the app tells you why in the folder bar. Nothing else changes.
If a folder looks empty
When Lumeira has no permission for a folder, it says so. It does not say "no images found". If you do see "no supported images found", the folder really has none the app can read.
Where the memory lives
Permissions are stored as security-scoped bookmarks in the app's own container. They are not sent anywhere. Removing the app removes them.