Qt does have an implementation that targets mobile. I don’t know how the licensing works, but in theory there should be a way to rely on Qt for mobile to extend support to iOS and Android. Way out of my own expertise, though!
Qt for Android and Qt for iOS can be used under the LGPL[1]. The issue for iOS, though, is that Apple's App Store violates the terms of the LGPL. To comply with the LGPL, you must make available to iOS users versions of your app that can be linked against user-provided Qt libraries.
If you use the Qt commercial license for either, then you don't need to worry about your app conforming to the LGPL.
