The name “Live Update.exe” is used by various companies, usually for software to check with the publisher’s server to apply updates.
It tends to install in a subpath of “C:\Program Files” ending with “\%Publisher Name%\Live Update\”.
I check all running processes regular on the computer systems that I use to make sure that the system is safe and that nothing slipped by the defenses.
While that works well, I usually spot processes started by third party programs after installation.
Your computer manufacturer may have altered the features, incorporated customizations, or made other changes to your driver.