Over the holidays, Lightning Returns: Final Fantasy XIII got some love on PC with a new patch that adds support for extra high resolutions. Six new ones in total are now supported: 3840 x 2160 (4K), 3200 x 1800, 2880 x 1620, 2560 x 1440, 2400 x 1350, and 2160 x 1215. Note you can't select a higher resolution than your monitor supports for supersampling purposes.
As well, in response to negative user feedback about not being able to boot the game in Offline Mode, you can now do just that. Square seemed to think Steam Cloud support meant Offline Mode couldn't be supported too, but now all is clear and the game can be booted regardless of whether you have a connection or not.
Hit up Steam for the patch.