I extracted the program to my hard drive but I don't see the LZH files to drop in the c: directory. Did I do this right or is there somthing I am missing?
There is no LZH file. That's a different archiver.
The LZX 1.21r1 archive on aminet includes several versions for different CPUs (It also includes an extract-only utility called unlzx):
1) LZX_68000EC-r
2) LZX_68020r
3) LZX_68040r
If you have a 68000 or 68010, copy (1) to your C directory and rename it LZX
if you have a 68020 or 68030, copy (2) to your C directory and rename it LZX
if you have a 68040 or 68060, copy (3) to your C directory and rename it LZX
Whichever one you use, be sure to copy the LZX.Keyfile to your L directory
After that you should be able to extract lzx files.