May I ask why you need to run your Chromebook with the lid shut?
1. I want to plug in my external monitor and use my Bluetooth keyboard and in essence use the Chromebook as a desktop unit.
2. I want to plug in my tv via HDMI and use my Chromebook to stream video content to the television.
It works with the Chromebook open, of course, but it just looks silly with two screens showing the same thing, so I turn it to the side which also looks silly. It would be so much easier if I knew how to disable sleep mode so that I could run it closed. And actually since one of the recent updates it does it (sometimes) automatically when I plug in the external monitor cable but not always. Haven't tried it yet with the HDMI since that update, but hoping that there is a way to do it manually.