In Windows 7 and LO v3.6, when I switched the input language via the Windows hot key (or Windows language menu), LO switched the input language in Writer. This worked geat for me to be able to write in multiple languages.
Now in Windows 8 and LO v4, this does not work. (Windows 8’s switching works fine with other software, so it is not a Win8 bug.)
I have confirmed that the “Ignore system input language” option is UNchecked (in Tools Options Language Settings), so apparently that check box is not working. (LO acts like it is checked.)