I'm new here! So forgive me if this has been posted before.
Well one of the shocking experience when I first got the A7 was the less than stellar battery life. Wifi is one of the culprit which I have switched off unless needed.
I have discovered that you can switch off the LCD monitor (well somewhat) by assigning a custom button to it. Basically it shuts of any preview unless called upon. It's not full off as the usual info still shows up in the black-screen. Hopefully it would reduce further drain.
Note: this is not the same as FINDER/Monitor setting.