I was using an external Lilliput monitor with the 7D for the first time and I noticed the camera battery were consumed much faster than normal. Is that normal? The monitor has its own battery! Does the HDMI signal in itself consume energy from the camera?

My thought is that it probably requires the camera chips to perform additional or different encoding than what is going to LCD, once the HDMI port is activated, so why wouldn't you expect a different battery usage. I had never considered that with my 5D, but now that you mention it, I do seem to see faster batter exhaustion when I am plugged into my Marshall monitor.

I've had the complete opposite experience. I use a 7D and Lilliput monitor with its own external battery all the time. The Canon battery now lasts MUCH MUCH longer because the 7D's own LCD screen is off, passing the signal into the Lilliput LCD which is powered by its own separate battery.

The one time I used the 7D without the Lilliput, I noticed the Canon battery drained so fast. I smoked through my Canon battery stash so fast that day and had to recharge four Canon batteries just to have enough juice to run through the day.