Install Latest OS X version with Internet Recovery
Do you have a Mavericks recovery partition? Or is Internet Recovery your only option?

From OS X: About OS X Recovery


If you use the Recovery System stored on your startup disk to reinstall OS X, it installs the most recent version of OS X previously installed on this computer.
If you use Internet Recovery to reinstall OS X, it installs the version of OS X that originally came with your computer. After installation is finished, use the Mac App Store to install related updates or later versions of OS X that you have previously purchased.


Source



To reinstall Mavericks, you can either create Mavericks recovery media or install Lion and upgrade to Mavericks.