Is it unusual for a three năm old cakapoo to just be lazy and lay down all day?

No,it's not.Dogs at that age should be excited,but maybe your dog is bored,teach it how to have FUN!And have fun with it!

I guess not. Maybe it needs excitement. Take it to the dog park.

yeah, if u don't take him much

Sounds likea common case of đi văng potato.