Actually, there was no simple way to use the original zzlib code, as there is no standard library available on the PICO-8, and some significant changes in the Lua language to make the original code unusable. Those changes include the bitwise operations, the 32-bit 16.16 fixed point format for storing numbers, and the peek/poke calls to access memory directly.
As usual the code is on GitHub. Also included is an example program that depacks a compressed image from the graphics ROM to the frame buffer, along with a tool (in Lua!) to build cartridge files from scratch, which allows to specify different input files for the different cartridge sections.
Also as usual, the code is free software, distributed under the WTFPL license.