FOTR wasn’t a complete DI, which is part of why the EE BR is so different compared to TTT and ROTK (which were complete DI’s). So at least some film would need to be scanned again for FOTR.
As for the other two, I’d assume it would be a 2K upscale with an HDR grade, just like the vast majority of modern CGI-heavy films already are on UHD BR.