Hi, I have the same issue! I've been searching for a solution for a while without success.
I have contacted the LG support and they confirm to me that there is no voice call function through bluetooth headsets.
My model is LG G2 (Stock SW Version D80210a-EUR-XX).
The following are the attempts have made:
http://xdaforums.com/showthread.php?t=2476080&page=5 (post 43)
NOTE: I have Google Now instead of Google search and I use Cyberon Voice Commander instead of Voice Dialer
-I've tried Bluetooth Launch
-I've tried VoiceDialerLauncher.apk (Post 10 Quote: "It is because phone launch MIC_VOICE_COMMAND intent action instead of VOICE_COMMAND. I wrote small application that intercept MIC_VOICE_COMMAND and run VOICE_COMMAND. I tried it with motorolla Voice Commands (installed on system partition) and it is works fine.")
-I've tried Tasker AUTOVOICE!
I think the solution is quite simple, for example with an xposed module, but we have to make our request to be take into account seriously.
Please keep us in touch if we found a solution!