Not sure if you have successfully solved the scanning problem with your Lexmark. By the way, I have EXACTLY the same issue with my Lexmark MX410de which can NOT scan but instead prints only on Ubuntu 18.0.4. I have tried installed the recommended drivers from Lexmark site for this particular Ubuntu version but no success. No scan utility application will detect my Lexmark as scanner and it will pop out message 'No scanners detected.
However, after downloading all recommended Lexmark Network and Scan driver 64-bit/32-bit Linux distributions with Debian based packaging from the Lexmark site, I figured out that there is NO support for the latest Ubuntu platforms. That is, I read the supported platforms text file for each package on the files I downloaded which say that the support is until Ubuntu version 12.04, 12.10.
Just read the supported platforms text file as follows
Lexmark Network and USB Scan Drivers for Linux Systems
Supported operating systems are listed in the table below. Make sure you
are running one of these systems before you use this application.
Linux Operating System Versions Hardware
Debian GNU/Linux 5.0,6.0,7.0 Intel (IA-32/64)
Fedora 17,18,19 Intel (IA-32/64)
Linpus LINUX Desktop 9.6 Intel (IA-32/64)
Mint 10,11,12,13 Intel (IA-32/64)
openSUSE Linux 11.4,12.1,12.2 Intel (IA-32/64)
PCLinuxOS 2011.9 Intel (IA-32/64)
Red Flag Linux Desktop 6.0 Intel (IA-32/64)
Red Hat Enterprise Linux WS 4,5,6 Intel (IA-32/64)
SuSE Linux Enterprise Desktop 10.0,11.0 Intel (IA-32/64)
Ubuntu 12.04,12.10 Intel (IA-32/64)
Thus I do NOT think there is a point make the Lexmark MX310 work as a scanner whereas it works fine as a printer! Also have a a look at this old link which shows particular Lexmark scanners supported which does NOT Include your model
Lexmark Supported Models for Ubuntu
Good luck and success if you have not achieved any progress so far.