I don't believe it has anything to do with your liver. Look up "microscopic colitis" on the internet. You need a biopsy of your colon (during a colonoscopy) to diagnose it. Your colon will look normal during the colonoscopy, but it's a disease which makes it difficult for your colon to remove the water from the waste. Those suffering from microscopic colitis can have diahrea for years, even indefinately. Ash your doctor about it. I am having the same symptoms (diahrea for 7+ weeks, 3-4 times a day) and my GI doctor took a biopsy during my colonoscopy yesterday. I'm hoping to have results soon.
Have you tried changing you diet? What if you AVOID dairy completely. Dairy is rough on us as we get older, I know that I get diahrea if I have any.
Frankly, I did everything I could. I eat lots and lots of fibers right now. I also had this lower back pain for about 3 years. I try to follow the mystery diagnosis on discovery channel. I just wish mine is not some rare diseases.