Nope, Lazarus runs on any system (Windows, OSX, Linux, Unix) and can compile the source code to any of those also. So you can write the program/app in (say) OSX and compile it to run on Windows / Linux / Android / iOS. Here's a tut on setting up the android ties for the Windows version of Lazarus: http://wiki.lazarus.freepascal.org/Android_tutorial
Officially you'd be better served (in Android) if you write the app directly in Java, from my experience the best IDE to use for Java is Eclipse. For iPhone it would be preferable to use Objective C instead (though Swift is a new language Apple made to use in their XCode IDE). And then if you want to also make your app work for Windows Phones you'd have to re-write it in some DotNet language like C#/VB-Net, i.e. VisualStudio. My issue with going about it this way is that you need to write it in 3 different languages using 3 different environments. That's one of the most awesome reasons to go with something like Lazarus instead.
Another alternative is to use Xamarin Studio. In this case you can write for all three mobiles using the DotNet platform instead. I.e. similar to Lazarus but using C# instead of Pascal. Note though Xamarin's not entirely free / open source - especially for mobile development. And then you could always go with Qt, essentially does the same as Xamarin / Lazarus but geared towards writing using C++.
Most other cross platform development for mobiles is done using html with javascript, or through the html5 idiom (basically just an updated version of the older html's DOM with JavaScript). Though this might not give the most awesome performance since it would basically run through a web page, so I'd think twice about creating some game using these. A nice IDE (open source) if you want to go this route is Cordova, but there's a commercial version with more capabilities called PhoneGap.
If you want to make some truly awesome 3d games though you might want to take a look at Unity. It's based on DotNet, especially through the open source Mono DotNet engine instead of Microsoft's - thus it works through MonoDevelop / Xamarin. Basically it gives a unified interface to the various 3d graphics for all systems / acceleration. So it would use Direct3d on Windows and OpenGL on OSX/Linux and OpenGL ES for Android/iOS.
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