Can anybody give pointers how I can implement lzw compression/decompression in low memory conditions (< 2k). is that possible?
If the choice of compression algorithm isn't set in stone, you might try gzip/LZ77 instead. Here's a very simple implementation I used and adapted once:
ftp://quatramaran.ens.fr/pub/madore/misc/myunzip.c
You'll need to clean up the way it reads input, error handling, etc. but it's a good start. It's probably also way too big if your data AND code need to fit in 2k, but at least the data size is small already.
Big plus is that it's public domain so you can use it however you like!