No idea about 32 inchers, but my Samsung has no issues with mkv, except for playing subtitles that are embedded in the mkv. If you extract the subtitles as srt, It uses them without issue.
Also to be a stickler, mkv is just a container not a codec/format. You should be able to extract the mp4/avi/etc file from that file.
I have the UN55D6050, 2011 model. If it supported it back then, I'm sure the most recent ones would handle it just fine.
What model year is your LG? Perhaps the newer ones handle MKV better? Also, I'm sure the playback support is based on model line. The cheaper ones don't have smart features or lack usb ports, while the more expensive ones have full support.