How do i transfer my Lime Wire library to my I-tune Library?

This is one of the most Frequently Asked Questions and the answer is easily available by spending a moment or two browsing the forum. Please check through the forum's wealth of information before asking another question.

However, since you are here you could:

Launch the downloads from inside Limewire (assuming that iTunes is the default format for your internet downloads);

double click on the MP3 files inside your Shared folder (assuming iTunes is the default format for your internet downloads);

drag your MP3 files from your Shared folder and drop them on to the iTunes window; or

use the menu command Add to Library in iTunes itself.

You may discover other methods by browsing through the forum if these suggestions do not match your requirements.