From what I remember of the 80's, LZH stood for Lempel-Ziff-Huffman, and referred to the compression methods employed by the archiving program. Many archiving programs would create .lzh files, but only LHarc would create .lha files, though it was possible for one decompressor to decompress both types of files, so they may have been identical, or similar enough for 8-bit computers to deal with it.
This Wikiepdia entry states that it was developed in 1988, but I'm not sure that date is completely accurate. I used LZH/LHA archives on my Commodore 64 for some time before I ended up switching from C-64 to IBM-XT in January, 1988. In fact, I remember being frustrated at not being able to find a decompressor for DOS that could read my C-64 .lzh text files.