But both definitely non-lizards.
I think it makes complete sense to confuse fish and birds based on movement, as you said.
I think Lukas has a different system, birds and non-birds. Well, and things he thinks are dogs, which unfortunately seems to include horses and cats.
I saw a nature documentary last night where the penguins were definitely flying - filmed from below under water it certainly looked like they were...
I think the problem is you misinterpreting the signs. What makes you think they mean "fish" and "dog"?
It's entirely possible that I've got it all wrong. The only animal sign he uses is one for birds, and that one we seem to be in agreement on. Either that or he is using it to mean something like "my hands are cold" and we are just bad parents. For dogs (and other 4-legged mammals) he attempts to bark. I had nothing to do with that one.
So Lukas is turning into a dog lover! :) Let me know if you need advice on choosing a pet.