you ask them for the LGPL package, they send it to you, you compile ?
The onus is on the person making the app that links against the LGPL library to provide you with the build instruction.
At worse they would give you their main static library and Qt LGPL source code and you just have to relink them and open Xcode to upload it to your iDevice ?
Here is for instance the source code for the telegram app for iOS which is under GPL : https://github.com/TelegramMessenger/Telegram-iOS
there is no difference with... basically every other open source project ? Open the .xcodeproj, build, run.