Ok, so I have contacted Lexmark and they have provided the following solution:
In X23xx and X26xx models the only way to let the user successfully install driver on so called NETBOOKs is to do the following:
1) You need these two scripts, and must copy these two scripts right beside where the "lexmark-inkjet.deb.sh " installer is located.(See attached file: extracter.sh) (See attached file: deb2lpia.sh)
2) open terminal and go to the location of the Lexmark installer, and do:
in the terminal do ---> sh ./extracter.sh lexmark-inkjet-09-driver-1.0-1.i386.deb.sh
result, this file gets created ---> lexmark-inkjet-09-driver-1.0-1.i386.deb
3) Rename lexmark-inkjet-09-driver-1.0-1.i386.deb to installer_i386.deb
by issuing the following command at the terminal ---> mv lexmark-inkjet-09-driver-1.0-1.i386.deb installer_i386.deb
4) please then do ---> sh ./deb2lpia.sh installer_i386.deb
result is this file gets created installer_lpia.deb
5) Finally, at last, do ---> dpkg -i installer_lpia.deb
That's it. The driver should be successfully installed and got registered into the synaptics record database ( which means, you can open synaptics UI, and can find our driver in the group called "notfree ").
I'm going to test this out shortly (but expect it to work) and will post to confirm if it worked.