First go to the options in Limewire and see where the songs are being downloaded to.

Then go to that folder starting at partition that is being used (usually my computer and the C partition) and click on the correct folders until you get to the folder which holds all the downloades.

If you can not get into that folder because you do not have access to the folder.
For example because you are not an admin. Then I would sugest changing the folder to which you download to. Preferable make a new folder in your my document and use it.

If you would like more than just your users name to have access to it then I would sugest putting the folder at the same level as my programs(click on My computer and then C, make a new folder).