What do the later builds of LAME do?  Is there any real-world benefit in CW updating from LAME 3.97 to 3.99.5?

Bug fixes. One that shows up occasionally here is a problem with VBR encoded files misreporting their run length.

The LAME updates provide lot's of bug fixes, as scook points out, but also they include usability enhancements and features that affect quality and speed of encoding. You can see what each update addresses by using the following link. Pay special attention to the features and fixes colored in red.
 
That VBR problem was fixed after 3.97. And there's a significant quality enhancement coming with the release of 3.100.
 
http://lame.cvs.sourceforge.net/viewvc/lame/lame/doc/html/history.html?revision=HEAD
 
Generally speaking, bug fixes and feature enhancements are desirable just as they are when users want SONAR updates.

the cakewalk version for some reason produces MP3 that my Boss micro BR does not like.  (the MP3 file works on the computer and mobile phone, but not on the micro br).  I tried various options, disabled VBR, different bit rates, etc.
 
but the current lame, version 3.99.5 (as an external encoder) produces MP3 that plays on the Boss.
 
I know there are issues with the Boss (google search will highlight this), so this is not entirely the fault of the Cakewalk version of MP3 encoder.

Is this something that comes with X3? I'm already able to export to MP3 and the quality is good.

Yes, sort of.
All Cakewalk DAW programs come with a 30 day demo. To use it after that, you have to pay a nominal fee. This is to cover the licensing fee that Cakewalk pays. You don't have to use it, but it allows you to export directly from X3 to MP3.

I had used audacity's mp3 converter but disliked the sound quality. I felt that there were some distortion in it. I paid for CW's mp3 converter and has been happy with it. Fast and easy, short and sweet.