[jpstewart]

I got GraphicsMagick to work by cheating, as it required liblzma.so.6 to work and this lib file isn't available in nekoware, so I made a copy of liblualib.so.5 (an arbitrary lib file) and renamed it to liblzma.so.6 and it now seems to work perfectly!
[...]
I've read that liblzma has to do with lossless data compression. I don't know where this would actually be needed by GraphicsMagick?

The GraphicsMagick README says:

GraphicsMagick requires the liblzma library from XZ Utils available from

   http://www.tukaani.org/xz/

to support TIFF with LZMA compression and future LZMA-compression features (yet to be developed). The utilities from this package are also necessary in order to decompress GraphicsMagick packages distributed with ".xz" or ".lzma" extensions.

Personally, I don't think LZMA-compressed TIFFs are common.  The TIFF format supports several other compression methods (both lossless and lossy) which are, IME, more widely used.  So, as long as you don't try to read/write such TIFF files you'll be fine without the library.

That said, are you sure liblzma.so isn't in Nekoware?  I think it would be part of the neko_xz package, specifically in neko_xz.sw.lib (which may not be installed even if other parts of neko_xz are).  Also, you may need the neko_xz version from beta instead of current.