Source: avforums.com

I use eac3to http://madshi.net/eac3to.zip and its gui ('yr_eac3to_more_gui' http://www.mediafire.com/download.php?nnomzlmkgz0 ) to extract and convert the audio to ac3 448 kbps...then remux both using tsmuxer http://www.videohelp.com/download/tsMuxeR_1.10.6.zip (add original mkv file, uncheck the dts audio and then add your newly created ac3).Leave as .ts extension also.My Lg plays the resulting mux(3d and 2d perfectly) and in sync.
Be aware that some mkvs have high level 5.1 and dont play (on my LG), on those i downgrade using tsmuxer to level 4.1(tick option).
Let me know if it works for ya :-)

Guide for mkv,how to play them all

OK...
SO YOU FOUND A NICE VIDEO BUT YOU CANT PLAY IT...
99,9% IT IS BECAUSE:

1)PROFILE IS 5.1 AND LG PLAYS ONLY =<4.1
2)SOUND IS DTS 

YOU CAN USE ANY VIDEO CONVERTER BUT 99% YOU WILL LOSE QUALITY ON BOTH VIDEO AND AUDIO,PLUS YOU NEED 2 MANY HOURS.

I WILL SHOW YOU THE EASY AND FAST WAY:-)
FIRST YOU NEED MediaInfo 0.7.52 - VideoHelp.com Downloads
TO SEE WHAT IS YOUR PROB.
LETS SAY YOU HAVE THEM BOTH...PROFILE IS 5.1 AND AUDIO IS DTS.
WE MUST DOWNGRADE PROFILE TO 4,1 AND AUDIO TO AC3 5,1.
FIRST WE CHANGE THE AUDIO.
YOU NEED http://www.videohelp.com/tools/MKV2AC3
ITS A AUDIO CONVERT TOOL,CHECK AUDIO OPTIONS TAB TO METHOD,ITS IS TO AFTEN BY DEFAULT AND NORMALY WORKS BUT SOMETIMES YOU NEED TO USE EAC3TO,ITS MORE POWERFUL TOOL.
DOWNLOAD IT http://www.videohelp.com/tools/eac3to
INSTALL IT AND SHOW TO MKV2AC3 WHERE IT IS,SO IT CAN USE IT.
JOB DONE,YOUR AUDIO NOW IS CONVERTED AND READY TO PLAY.
NOW ITS TIME TO CHANGE THE PROFILE.
YOU NEED http://www.videohelp.com/tools/tsMuxeR
TICK THE CHANGE LVL TO 4.1 AND START MUXING...
JOB IS DONE FAST AND EASY,YOU HAVE A VIDEO THAT PLAYS TO YOUR TV!WITHOUT ANY VIDEO LOSS QUALITY AND DOLBY DIGITAL SOUND!

MACOS AND LINUX USERS MUST USE OTHER TOOLS,SORRY.