Thanks, to HDMI 2.0, there should now be enough bandwidth available for 1080p 240 Hz input. From there it should be relatively straight forward for a display to do simple dot-double scaling to turn the 1080p into 2160p (4K UHD). Yet I haven't seen any talk about it. Perhaps there is a technical issue I am not aware of?
Seems like almost every 4K TV coming out in 2014 will have HDMI 2.0. There has been some talk of 240Hz refresh rates on 4K TVs like the LG UB900 Series. But nothing about 1080p 240 Hz input specifically.
http://hdguru.com/lgs-2014-lcd-uhdtvs-announced/LG’s UB9800 Series consists of models with 65-, 79-, 84- and 98-inch screens. These sets have a 240 Hz refresh rate and a Harman-developed multichannel audio system (4.2 channels on the 65-inch, 5.2 on the 79-inch and 7.2 on the 84- and 98-inch models).