When I read the title, I honestly thought this was an official LEGO thing. This is exactly why it's important for a company like LEGO to protect its trademark.
I realize this is just an homage to LEGO and I'm sure they know and appreciate that. But they still need to defend their trademark. If they don't, anybody could just use their name for whatever they wanted - even things they DO NOT want to be associated with.
There actually used to be a "legOS" project (homebrew firmware for the original Lego Mindstorms) and they were politely but firmly asked to change their name.
Trademark infringement requires a bit more than just using the name (likelihood of confusion is one of the tests), but given that companies need to aggressively defend their trademark to keep it they might file a suit anyway.
I get how that would happen if a company used the name commercially, but wouldn’t this be classed under fair use as long as the usage was non commercial? Anyways, IANAL.
(INAL as well, but as far as I know:) Trademark fair use is different from copyright fair use. In short trademark fair use is if you use it to reference the original (e.g., "compatible with WindowsTM") or if its not used as a trademark to describe your service. (WD-40 example I found used "inhibitor" while "THE INHIBITOR" was trademarked)
Patents are entirely unrelated to trademarks. I very much doubt that an operating system would be able to infringe on a patent for interconnecting plastic blocks.
An operating system called "LegoOS" might infringe on the trademark of a plastic block company called "LEGO" (though one of the tests is "likelihood of confusion" and it would be hard to confuse the two).
I used to work for LEGO. They have more lawyers than I've ever seen anywhere else.