I wasn't aware of some peculiarities of the LGPL. Instead of reading the license itself, I went for
the Wikipedia page, which seems very complete.
The first thing is, unlike the GPL, work derived from the LGPL doesn't need to be totally LGPL too. You don't have to use the same license for your code, but it should be possible for the user to change the LGPL parts and recompile, so you have to provide
1- the proprietary part as a linkable object, or
2- the code, even under a proprietary license.
Do any of you guys know how to make such a linkable object? It seems easier to provide the code. Showing your code is not the same as allowing anyone to use it as they want. For example, the Ludum Dare competition demands that competitors show their code, so that some disputes can be solved, and yet the author still has all rights to it.
As Arduino istelf has shown, it's possible to have more than one license in the same repo, but it has to be clearly stated what is what.
Ok, let's split this in parts.
gamebuino_boot was based on official Arduino code (LGPL) and some parts by thseiler (license not stated). Regardless of whether thseiler's code is based on Arduino or not, his permission is necessary. When that is solved, if the bootloader code never gets into a game, I think that the best license for the bootloader would be GPL. However, if there's a chance somebody might use code from the bootloader in their games, it's best to keep it LGPL.
libraries/tinyFAT is clearly marked as LGPL which seems to contradict the CC BY-SA stated in the main readme. Also, it looks like it came from somewhere else, but the author's name isn't stated anywhere. Maybe it's official Arduino code?
libraries/Gamebuino: is there any Arduino code in this folder? If so, is it in separate files, or totally mixed up with Gb code? If you're going to LGPL the whole thing (which is probably the best option), then it doesn't matter. If they're going to use different licenses, then they have to be clearly separated. Keeping it LGPL is simpler, and it's permissive enough so that these libraries can be used in proprietary games. Sure, using, say, MPL would be simpler, but that's no good if part of the libraries is already LGPL (that is, gamemakers will have to provide compilable parts).
And... I don't know about the rest, but this should help figuring out if anything has to change there.