Thank you for the responses. I guess the LG BD390 must not support embedded subtitles over DLNA. I will confirm that with LG support. In the mean time, it looks like I will just need to extract the subtitles from the MKV and allow Mezzmo to stream them externally.

The option to transcode and burn the subtitles into the video is not very appealing to me, because I want to be able to turn the subs on or off at will. So extracting them and streaming them externally is probably the best option for me.