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WHICH IS CORRECT? WHY IS THIS LYING AROUND OR WHY IS THIS LAYING AROUND?
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In this particular sentence, it should be "lying" (from to lie, to be in a horizontal position). "To lay" is "to put down", so it doesn't apply here.
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Lay is an active verb: it implies that somebody is setting or placing something somewhere.

Ex: He will lay the book on the table.

Lie is a "still" verb

Ex: You lie in a bed.
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Comments  
To confuse the matter a bit more, the past tense of lie is lay. The past tense of lay is laid.

e.g. He lay on the couch and fell asleep.
Students: We have free audio pronunciation exercises.

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It depends on what the speaker really wants to say. I you use "lying", that would mean to lie down. If you use "laying", that would be putting something down. The man is lying around the house means he lies down the couch or sofa. The hen is laying around the barn means the hen keeps on laying eggs.

I hope il be of help ^_^
Resident found on the floor lying in a supine position.