Ugh, tell me about it. I learned that the hard way after a bouquet for my mom turned into a slimy mess overnight. Those pretty tiger lilies basically melted a bunch of white carnations right next to them. The water got all cloudy and the other stems felt like gross, slippery noodles. You don't forget a flower murder scene like that.
My sister's wedding flowers were a total loss because of lily sap. The roses in the centerpieces wilted into brown mush within a day. The florist had to do a full emergency replacement.
Really though, how common is this? I mixed some lilies with daisies last month and nothing went wrong. The water stayed clear and everything looked good for days. Maybe it's only certain lilies or a problem with older flowers.