LEGO trademark registration
https://trademarks.justia.com/745/93/lego-74593028.html registers the trademarks also in all the major categories where software can fall in, and so it's upon LegoOS to demonstrate that there's no way that an uninformed consumer might confuse and think that they're related (which is IMHO impossible, given a single look at their homepage).
It also explictly lists that the trademark is used (among other things) for educational computer programs, computer accessories, entertainment services in the nature of providing facilities for playing computer games, conducting workshops for instruction in the use of computer software, etc - and that's true, I personally know a bunch of software products with the LEGO™ brand.
As the trademark is both used and registered not only for plastic bricks but also in the field of software, naming a product LegoOS by itself would invite a trademark claim, and putting a red brick (that's not registered, but definitely does create an association for the average consumer, which matters very much in trademark claims) on the homepage just removes any maneuvering space; IMHO it'd be a slam-dunk guaranteed immediate injunction if LEGO sends a C&D that gets contested. And the practice of trademark law means that they pretty much must sent a C&D, not doing so would be quite bad for them.