A rhyme helps to remember how to keep watch on the lions. It is said that...
"When the lions drink, London will sink"
"When it’s up to their manes, we’ll go down the drains"
"When the water is sucked, you can be sure we’re all ... in trouble"
So if the level of the Thames reaches their mouths, we are at risk of a flood. Thankfully, it hasn't yet. The rings were, we are told, designed by Timothy Butler and installed as part of Sir Joseph Bazalgette's Victorian sewage works programme in 1868-70.
For more on superstitious flood-watching, see here.