/SNIP/
So in the case of "The body lay/lie in the grassy field," they'd both be grammatically correct, but in different tenses. There's no direct object, so you know you want the base to be "lie." Except, if the narrative tense is in past tense, you'll want to use "lay" because it's the past tense of lie.
Present tense: "The body lie in the grassy field."
Past tense: "The body lay in the grassy field."
Yeah, I still get confused over that one sometimes too.
Cannot completely agree with the present tense part- it depends on singular versus plural.
"The bodies lie..." Present tense, plural. The bodies are there right now.
"The body lies..." Present tense, singular. CF- "My bonny lies over the ocean...". (Which when I was a kid, I thought was "body.")
However, past tense doesn't seem to care about singular/plural- "The body (or bodies) lay in the field until the families came to collect it( or them).
Here are the inflections: "She is going to lie down. She lay down. She hasn't yet lain down."
"Lay down your sword. I laid down my sword yesterday. The weapons had been laid down."
The sad part (and what makes these things hard for me to explain clearly), is that I tend to do this "by ear." And being a doggie, I have really good ears.