"A dog is lying on the ground."
Translation:На земле лежит собака.
Yeah. It's not as simple as subject first = "the", subject late = "a', but both of those things developed to solve the same problem: to tell people what in your sentence is new information, and what is just connecting things already mentioned.
If you say собака first, that sounds like the dog is already established as a topic of conversation, so you're telling someone where some dog is which you were already talking about. If you put it at the end, it sounds like the dog is new information, so it can't be "the dog", which is a dog that's already part of the conversation.
Firstly, "to lie" does not have to be an action - it can be a state: you lie in your bed while asleep, no action involved. (Don't mix it with "laying something down" which is always an action, but is inapplicable here).
But in any case, action or not, собака here is a subject, not an object and hence should be nominative.