Updating the LG P705 to Android 4.1.2 (or later)

I have an LG P705 phone which comes with Android 4.0.2 installed, and the OS is badly out of date. The LG updating software, however, says that the phone is up to date. I've been poking around XDA Developers, but the jargon, malformed English, and references to many different phones leave me quite confused. I get the impression that it would be helpful to root the phone, but I haven't yet found clear instructions on how to do that. An extra complication is that a lot of the files out there seem to be infected with malware.

I'm running both Kubuntu 14.04 and Windows 10, and I've installed adb on Kubuntu (and used it to access the SD card).

Is it possible to update my phone to 4.1.2? And if so, how?

 

So where can I find instructions on how to do that?