I wrapped together a BlitzMax module for LZMA compression. It is based on LZMA SDK (version 4.62) and only has a BlitzMax wrapper written by me - the rest is someone else's work. It is completely in the public domain.
There are two releases for this. The source only version requires building modules whereas the Windows build does not (but obviously only work on Windows).
To install, simply unpack the zip to BlitzMax/mod. The test.bmx file included can be used to test it works and shows how to use it. The interface is like that of Pub.Zlib which comes with BlitzMax by default.
Coming up next: LZMA streams...