Is it ok to keep lettuce in water in the fridge?
I don't see any reason for it to be unsafe. 

However, I think you are wrong in assuming it will keep longer. I keep my lettuce in a closed container with water on the bottom, then a trivet, then the lettuce on the trivet, raised above the trivet, and the whole thing in the fridge. It keeps that way for weeks, not getting yellow, and not wilting too much. 

If a leaf falls into the water, or the water is so high that the bottom of the lettuce touches the water, these parts rot within 2-3 days, not unlike how the leaves of flowers rot soon if submerged in the vase while the leaves and blossoms above the water level keep well. So, I don't see why you would place the leaves in water on purpose. Since the rot is easily perceivable, I would say it's safe (you won't eat it once it turns bad), but it is not really a good storage strategy.