I used to have a male Great Dane that could drink the toilet bowl dry. If he still wanted more water, he would drop the lid down so that it would make a loud bang against the porcelain. Then he would lift it back up and let it drop down again. He would continue this banging of the lid until I heard him and came in and flushed. I suppose I should have trained him to flush it himself instead of banging away at the toilet seat.
That Dane has long since passed. Now I keep the lids down, and I use a horse water bucket for the dog’s water. I fill it up and dump it several times per day so that they have plenty of clean, cold water. My dogs seem to prefer clean water in a deep bucket – they don’t like shallow pans of water where the other dog may have spit or drooled in the water or warmed it up. They used to drink out of the toilet, so I tried to create a system that was as close to the toilet as I could – filling a horse water bucket with cold water seems to do the trick.