But they're not making the patented invention; they're making a description (the source code) of the patented invention. They're distributing the source code. Hence the moniker: "Lame Aint an MP3 Encoder" (it's a description of one).
On the other hand, distributors of binaries do have to take into account patent laws.
That is their claim, yes. As far as I know, no one has ever tested this in a US court. I would not be hopeful. Also, the initial term "Lame Ain't an MP3 Encoder" referred to their use of the original ISO code along with a patch. Since one would have to use the MPEG/ISO code and you couldn't encode mp3 files only using the LAME patch/library, they avoided the patent issue. Since 2000 they have instead shipped source code with a complete rewrite of the ISO code. They also post a notice that an MP3 patent license may be required for use in some countries. According to the conventional interpretation of US patent law, the US would be one of them.
Edit: By the way, don't be fooled, our small legal disagreement doesn't affect my very positive view of you as a person and developer :)
On the other hand, distributors of binaries do have to take into account patent laws.