Have you tried scanning using the built in Apple app Image Capture, or tried through System Preferences> Printers & Scanners>Scan.
You could try resetting the printing system, If you can't print from your Mac or iOS device – Apple Support
scroll down to Reset the printing system. When you add the printer back in it should start looking for any new software.
Make sure you are on the internet when doing this.
If you look at the Lexmark website it only offers support up to macOS Sierra (10.12), so that would mean Mojave is not supported, but there were drivers listed as being for Mac OS X 10.6.8 and later OS's, so it might be worth downloading and installing them, have a look. There is also a firmware upgrade that was released in March.
http://support.lexmark.com/index?locale=EN&page=product&userlocale=EN_UK&productCode=LEXMARK_CX310#2
When the page opens click on the Operating System button, select Macintosh, and then you will be able to select
the version select macOS 10.12.