"I'm laying out in the sun."
"I think I'll go lay down."
"This is my dog laying on the couch."
However, Hoosier dialect still uses "lay" when appropriate.
"Lay that on the shelf over there."
"He hit him right on the jaw and laid him out."
For the record, the verb "lay" is a regular verb with past tense and participle "laid." It is a transitive verb, which means it requires a direct object. It can refer to yourself only when the action is being done to you.
"Now I lay me [me being the direct object] down to sleep."
"She laid the platter on the table."
"Lay it on the grass over there."
"The body was laid out for the wake."
The verb "lie" is an irregular verb with past tense "lay" and participle "lain." It is intransitive, meaning it is an action without a direct object.
"I think I'll go lie down."
"I lay out [past tense] yesterday, but I have no time for that today."
"I've lain on the couch all morning."
If you are in doubt about which to use, do this. Take your contemplated sentence, such as "He's just laying there" and ask, "He's just laying what there?" If that makes no sense, then neither do you.
Two final warnings.
Final warning 1. Both "lie" and "lay" are used as sexual euphemisms, but they are both used grammatically even in their slang applications. "Lie" is more antique and requires the use of a preposition or adverb such as with or together.
"Come lie with me."
"We lay [past tense of "lie"] together all the night."
"Lay" is usually met in participial form, often in a passive construction.
"He finally got laid."
Final warning 2. Both "lie out" and "lay out" are permissible constructions, but they are obviously not the same thing. One refers to suntanning and one refers to preparing a body for burial.
"I think I'll go lie out in the sun today."
"The undertaker came to lay old Mrs. Carrithers out."N.B. The use above, "He really laid him out," meaning "knocked him down/cold" is an adaptation of this expression.