Thisis my family's take on it. Different families might have different interpretations.
We're pretty sure lizards drink slowly. That's the point - it's over-cooked sardonic humour.
Sometimes when I meet up with friends or family in the middle of a heatwave I say, "brrrr it's a bit chilly" and we all laugh.
So the lizard drinking saying means going fast even though lizards drink slow.
But some folks (or maybe AI) who take things literally have written on the internet that lizards flatten out when drinking and people who are in a rush also feel flattened out.
The very few times I've seen lizards drinking, they didn't flatten out much as far as I could see.
@Ribh would know more about lizards than I do with all those monitors hanging around.