Learn English – Lying down or laying down

You are using the Present Perfect in your first sentence, but you'd need a duration phrase to make it more natural for this context:

He has lain on the ground for centuries.

Without that duration phrase, the reader might think that "at some period in his life he has lain on the ground, but now he's quite an active guy". This would be unfitting for a statue.

In the second sentence, I'd delete down:

He is lying on the ground.

With down, it might be understood that he is in the process of lying down: he hasn't yet settled in his position.

The third sentence is unfit because laid is the past-tense form of lay, not of lie. "Lay" means to "place something somewhere". It's a transitive verb. That's how we usually use "lay":

He has laid the flowers on the ground.

It's quite hard not to get tangled in the diverse forms of "lay" and "lie". Here's a related question:

• What is the difference between “lay” and “lie”?

The ELU StackExchange even has a special tag to mark questions related to the usage of lay and lie.

Here's a handy table with forms of lie and lay:

(from "Lie Lay Practice Worksheet", Freeology.com, licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 license)

Read also:

• LIE OR LAY? SOME DISASTROUSLY UNHELPFUL GUIDANCE - Language Log