Ah thanks guys. Didn't know there were different meanings in the laying down thing.. of course, needs to be put into context. Milo's a very submissive dog, so dominance doesn't seem to be the correct one. I think he was trying to say the other dog is getting over the top, but it just wasn't responding to it hahaha.
Dog behaviour is so interesting! I'm still guessing what's actually happening. I usually assume if the tail is wagging, then it's all fun and play.