Technical issue related to the opening of Lightroom app

Possibly you are not signed in to your Adobe account when trying to start Lightroom, so an internet connection would be needed for that. I've just tested on both iOS and Android, and the app starts OK with no interent connection, so maybe there's a periodic check of the Adobe ID credentials which would usually go unnoticed if there's normally an internet connection, but would cause the issue you have encountered when there's no connection.