So, it turns out the iTunes COM API is incredibly simple to use - even with C#. It's only taken me half an hour to write a little app that grabs the selected track from iTunes, searches a lyrics website to grab the lyrics, and adds the lyrics to the track info in iTunes.
Here's a screenie:
At the moment it's really basic - it will only work for one track. But it will be easy enough to make it work for any number of selected tracks.
Let me know if you're interested - I'm quite willing to publish the source and binaries.