Okay, here we go:
MP3 is a codec. LAME is an implementation of that codec.
Fraunhofer/Thomson holds several
patents relating to MP3. All MP3-related software makers must pay
licensing fees or else face patent infringement charges (not on the list: freely-distributable software decoders are not charged a fee). This applies regardless whose implementation of MP3 you're using - LAME, Fraunhofer, Xing or otherwise. Truth be told, anyone distributing LAME binaries (exe or dll) is infringing on Fraunhofer's patents if the patents apply to the person's home country. Do note that the LAME developers only distribute source code, which is what gets them around the patent barrier.
Why would anyone license Fraunhofer? Because of the LAME licence. Anyone developing around LAME must keep the LAME code in a separate shared library external to the main program or else license the entire program under the GPL, which is the last thing most companies want to do. They would also have to make available the LAME source and any changes they made to it.