I have looked at the sources of the Total Commander's LZX plugin and the implementation that @MiDWaN proposed from amiberry project.
It seems that the best bet is to use the implementation from amiberry, but someone will need to decouple it from the UAE first.
It is interesting that there is no actual library to work with LZX. For example, the LZX official site only contains a UNIX console unpacker, and its code can't be used as a library, because it mixes the unpacking logic with console output.