Thank you so much! I didn't manage to download the firmware, but will try again the upcoming days, and give you an update when I succeed with all of this!
Update: found some help with downloading the firmware in this thread: https://forum.xda-developers.com/optimus-g-intl/general/download-kdz-file-http-csmgdl-lgmobile-t3309957/page2.
After that the process was easy enough. I have only tested the CM13 for one day, but so far everything seems to work and I really love the system. My phone is the LG G3 beat (D722, jagnm). Thanks a lot for the help!!!
Here is the bootloader patcher for kitkat:
And here for lollipop:
If I remember correctly I have the patched LP one for D722 installed on my device. I can dump it and upload it if nobody else finds it.
take a look at this post, see if it has what you need...
su dd if=/sdcard/aboot.bin of=/dev/block/platform/msm_sdcc.1/by-name/aboot