Actually you can do almost just this but not in Limewire itself. You would need to add new downloads to iTunes, and have iTunes automatically sort into folders by Artist (provided the tags are filled in correcty
The songs would start off in the one folder, but it is a simple procedure to select them all and move them to iTunes.
If you use MacOSX it is simpler and easier, but I'm guessing you use Windows.
There is a sticky about just this under open discussion topics in Limewire (cross platform)
There are other third party players that will also do this, I'm sure