The context is
"The mercenaries lie/lay dead."
"The animal lies/lays dead."
It's present tense and there's a corpse involved.
I've looked it up elsewhere and I just don't understand the rules. Something about an object? Is a corpse an object?
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Simple enough, once you understand it. Not too simple if you don't.
To begin with, the answer:
If it is really the present tense, you must use lie(s).
Here are some of the difficulties:
This type of sentence is rarely used in the simple present. The simple present tense is only used when something is always, or habitually, so. But mercenaries always lying dead is not a likely scenario. This type of sentence requires the simple past if it already happened, in which case the verb is lay(s), or if it's happening now, the present continuous, in which case the verb is is/are lying.
There are three verbs with overlapping forms that confuse people: to lay, which means to put something down something, to lie, usually used with down after it, which means to assume a horizontal position, such as we do on a bed, and also a second verb to lie, which means to tell a falsehood. To make things worse, the past of to lay is laid, which is a word that is avoided by some people because it may be used as a somewhat vulgar slang term for having sex with someone. The past of lie (down) is lay (down), and the past of the other lie is simply lied.
You're confusing an everyday object with a grammatical object. An everyday object is just a thing...a pen, a hamburger, a hand. A grammatical object is something that receives the action of the verb, and usually follows it. It may be a thing or a person. Yo use the verb lay, we need a grammatical object, but it can be a thing or a person: "I laid my pen down". "I laid the baby down to sleep". Notice that if I myself did the same thing, there is no object in the sentence, and I'd say "I lay down, but I'd be using the verb to lie down in the past, not the verb to lay.