Is it just one file that's slow? Are you downloading a torrent or a file from the gnutella network? Does the file have one host or multiple hosts?

You can only download as fast as the other host(s) can upload... if they have a slow connection or heaps of upload slots open then you might be restricted to a slow download.
And if your ISP throttles p2p bandwidth then that can slow things down as well.

If it's happening with every file after updating to a new version of LW & you're sure that your ISP's not throttling p2p, try deleting LW's preferences folder when LW's properly closed.
See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
Vista users: LimeWire Pref Folder in Vista