Sorry for the triple post.
I check into files of the new SD card and there were two folders that looks like NAV program upgrade so I extracted them and tried to "install" them from USB via the debug menu (holding MENU + 3 times switch headlights).
First folder HC03, version works and shown as VD12106A (files last modified: 2019-05-20). This is the version that was installed in my car when I first inserted the new SD card so I could not press the update installation button.
Here is the link to download that version, it should be compatible on top of the previously shared one: VD12106A (2019-05-20).zip . (I downloaded the one from this thread and the version was shown properly, I could not install because I had newer already).
The other folder HC83, USB is detected, copying of files completes but then gives me a blank screen. The files are newer (last modified: 28-01-2021) maybe this is for MM15? My system is MM13 as I mentioned above.
I also upload the HC83 one but the version is unknown, all I know is that it was in folder HC83 and have been updated in 2021, someone with MM15 could try to see what version number is displayed but I get a blank screen.
Then regarding the other zip files I downloaded from the Lexus-Tech, they are not detected either via norma software update or via the debug menu.
Also filename is different than the one for nav system:
Bulletin files: 15LWENEU-BBXX_XXXX.KWI (I assume the one starting with 13 would work on my car? but they are not proposed to me in Lexus-Tech) Conclusion: These are not for the navigation/multimedia software?
Nav software update files: HASHLIST.DAT + LOADING.KWI (Assumed Multimedia/Navigation software (?))