Apple iOS IDE for linux?
What you are asking for is neigh impossible. The only solution I could think of to develop on Linux would be to use GCC or Clang to compile Objective-C. There are no Apple Frameworks or simulators, save GnuStep, and that isn't 100% compatible.
There are a few problems.
The iOS SDK libraries don't exist for Linux.
The simulator does not exist for Linux.
How do you plan to sign your app from Linux?
You could technically use a VM, but that is against the Mac OS X EULA. Another sketchy option is to compile against GNUStep and test on a jailbroken device.
Honestly, your best bet is to break the bank and get a Mac (Mini or Air, now that the MacBook is discontinued. That said, you might consider spending a bit more on a larger screen. It's really hard to write code on just 11 inches of screen.) A few moths of developing may make back your initial investment.
Good luck!
While probably not producing native looking apps, there are a couple cross-platform multimedia tool-stacks, like the Kivy Project - which supports packaging for iOS - http://kivy.org/docs/guide/packaging-ios.html - This project does use Python as the programming language, not objective C.
Take a look here for info on this. Basically, running a virtual machine with an OSX image is likely to be the best approach if you'd like to distribute your app through the Apple store.