The Cakewalk encoder is a commercially licensed version of LAME
More accurately the Cakewalk encoder is a licensed version of the MP3 encoding technique to which the Fraunhofer Institute, claims a patent. Lame is an independent implementation of the encoding technique, which may infringe that patent. Hence the rather strange behavior on the part of the Lame ("LAME Ain't an MP3 Encoder") Lame developers to only distribute source code in an attempt to avoid infringement action that they apparently expect would be more successful against compiled versions. The argument seems to be analogous to the distinction between distributing the blueprints for a mousetrap as opposed to manufacturing and distributing the mousetrap itself.
In any case the Fraunhofer and Lame MP3 implementations are not identical, although the resulting compressed audio works pretty much the same, and each version has its fanboys.