With the mark II you can only use one: lcd or external output. The mark III allows the lcd to stay on when an external hdmi source is connected. The mark II just doesn't have the horse power to run two video sources. An option you may consider is an hdmi splitter. That way you could run hdmi out to the splitter and then one line to a monitor attached to camera/rig and the second line you can run to a client or video village.
This also ignores the fact that the recording framerate of video out is 480p :/