LGPL requires that the user be able to replace the LGPL portion with an updated / modified version. This is usually accomplished with dynamic linking. Since the iOS store requires apps to be signed and disallows dynamic linking, there is no way for the user to modify the LGPL portion. I assume other app stores are similar.
GPL is disallowed for similar reasons, no way for the end user to recompile and app from the app store and run it on their device.
I believe Qt does offer a shared library for Qt that can be shared/upgraded across multiple apps. I wonder if that's enough to allow one to deploy on Android (iOS is obviously a no-go).
I have an early prototype in Qt that's not going to be a big bread winner, but it'd be nice to be able to release it and get some feedback (even if that means that they have to install the shared Qt package too). I'd probably just bail on the idea if I had to pay much of anything, especially monthly.
The plain GPL is usually said to be unusable on the App Store because it has a clause that "no further restrictions" may be made on the use of the software; that may be fine with you, but when Apple redistributes your app through the App Store, they do it with a EULA that prohibits a wide range of things, so, as the argument goes, such redistribution violates the license. The LGPL does not have such a clause, so it's OK. (It does have a clause that prohibits further restrictions on reverse engineering, but the iTunes terms of use have an explicit exemption to the general reverse engineering ban based on "licensing terms governing use of any open-sourced components".)
Also I believe you could make the object files (before linking) available on your website, and you'd still be fine. If I'm wrong someone please correct me.
GPL is disallowed for similar reasons, no way for the end user to recompile and app from the app store and run it on their device.