I don't have such a printer so I don't know if this'll help, but the problem could be 64 bit - you don't say... Also, I wonder if you are installing as per the Lexmark instructions as you mention CUPS - Lexmark don't and their driver is a deb file initiated in terminal. Finally, maybe use sudo in terminal when installing...
On top of all that, assuming you're running 32 bit Mint, have you tried re-downloading the Lexmark Z2300 driver lexmark-inkjet-08-driver-1.0-1.i386.deb.sh.zip from here
? Lexmark don't supply an MD5SUM so checking is moot, but it should be 29.91MB. I downloaded it: 31.4 MB (31366727 bytes)
The Lexmark printer driver installation instructions for 32-bit Linux distributions with Debian-based packaging is here
Hope this helps.