The best replacement for lzw is deflate.

The best alternatives to lzw are rated as following:
★★★★★  deflate
★★★★★  lz77
★★★★  gzip
★★★★  huffman
★★★★  packbits
★★★  ccitt
★★★  zip compression
★★★  zip tiff compression
★★  lzma
★  rle
★  zip tiff

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Google Trends

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lzw
deflate
lz77