I am working with a lexmark-inkjet-legacy-wJRE-1.0-1.amd64.deb.sh

Within the Downloads directory I did:

~/Downloads$ ./lexmark-inkjet-legacy-wJRE-1.0-1.amd64.deb.sh

The Lexmark Linux Installer box opened, and I proceeded with its prompts. At one point I had to enter the root password.
I then got the following output:

Verifying archive integrity... All good.
Uncompressing nixstaller.......................................................................................... .....
Collecting info for this system...
Operating system: linux
CPU Arch: x86_64
TRACKING IDENT = 140509
cpu speed = 2400 MHz
ram size = 1947.60546875 MB
/tmp = 8713 MB , /usr/local = 3387 MB

At this point it does nothing else; with nothing showing in the Progress Bar.

When I try to cancel it I get:

Install commands are still running
If you abort now this may lead to a broken installation.
Are you sure?

I answer NO, and then it still goes on to do nothing.(even 30 minutes later)

I'm no expert with drivers for hardware but I'm wondering if an unmet dependency is the problem:-

Aside from what you posted, are you getting a dependency message or why the configuration script is failing?

When you downloaded the driver (tarball) did it come with an "Install" file or a "Read Me" file? Maybe the Make or Build file is missing-

I'm thinking if it is still hanging after 30 min's something is most certainly missing or perhaps broken.

These Debian pages may be of some use:-

https://wiki.debian.org/SystemPrinting
http://packages.debian.org/wheezy/system-config-printer
http://packages.debian.org/wheezy/libcups2