A quick search of your model number turned up the manual, which sent me to go.roku.com/rokumediaplayer for a list of supported formats. DTS is listed, but it also specifically says:
Note: DTS-HD and lossless DTS are not supported.
So you’ll have to remux the MKV file with a standard DTS encode of the mix of your choice, or a Dolby Digital/AC-3 encode.
However, FLAC and PCM (.wav) audio are supported, so if you still want lossless you can remux your MKV with an uncompressed PCM encode or a lossless FLAC encode. I don’t have the mono mix in any of these flavors, but I’m sure someone can help you out with that.
Okay I installed Tsmuxer and opened the mkv file. I kept the mono track checked. How do I know that the output file will retain the same quality as the original?