Hi Anenu,
The solution to your worries is
very easy.
First, forget about iTunes. iTunes is just no longer necessary for
anything to do with your iPhone or iPad in 2013.
You simply convert your LIT files into EPUB files in Calibre. That only takes a few seconds per book.
Then, you can just email the EPUB files to yourself, and open them from the email attachment in Stanza or any other e-reader on the iPhone.
Or, my favourite way: just put those new EPUB files into Dropbox. Then, open the Dropbox app on your iPhone, and there they are! You can easily load any or all books into any e-reader on the iPhone, including Stanza.
Note that Stanza is dead, partly dysfunctional in iOS 6, and hasn't been developed for years. Stanza now has its successor on the iPad, called
Marvin,
www.marvinapp.com, but it will take a few more months before Marvin for iPhone arrives. In the meantime, I'm still using the (partly dysfunctional) Stanza in iOS 6, and in terms of nice rendering of texts, I also like the Chinese app
Apabi Reader.