I'm not sure if a standing desk is good for lower back pain (or if it's just good for preventing lower back pain by strengthening your back), but I just bought this adjustable standing desk thing for $40 and it's been helping quite a bit.
I've been working at home for the past 8 years. I'm in a similar situation as you where I end up spending 10 to 14 hours in front of a computer per day. I was having lower back pain as well. What relieved the issue was switching to a standing desk. I've been using it entirely for the past 11 months (got it setup in January). It's made a world of difference. It took about 2 months to get use to but after that there's no looking back. At first you'll get some foot fatigue from standing so many hours. Get a comfortable running shoe with tons of foot support or/and a standing mat. I got a cheap standing desk setup from amazon for about $30 and the mat for the same price. No need to spend hundreds of dollars setting up one.
For exercise, I'd focus on ones that strengthen the lower back. Your lower back is weak from all that sitting and it's this weakness that's making it feel tight and unconfortable. Throw some supermans into your routine. They gently work the lower back.
Also, I find regular theraputic massages helped a lot. If you can afford one, I recommend heading to a good one that'll take care of your upper body. They provided with lots of relief.
I'd wonder how that might compare to this one, which costs $40: http://www.amazon.com/gp/product/B00466887G
It's said to be a best seller, the average review is like 3.5 stars. Of course, I've never owned a standing desk before.
So you basically have a laptop the whole time, right? No multiple monitors? How would one of these go about with this?
https://www.standstand.com/store/
http://www.amazon.com/iCraze-Adjustable-Computer-Multifuctional-Ergonomics/dp/B00466887G
Do you have a good laptop stand for your bed so that you can lie flat on your back? I have a Levo floor stand for my iPad which works very well in bed. I sometimes use a bluetooth keyboard on my lap, for my iPad, so I don't have to lift my arms at all.