Native English speakers, could you please help me with these issues?

"They were so focused on their brawl, that they lost track of the imminent dangers around them."

I'm assuming there are multiple sources of danger around them, hence the plural. If there's only one thing near them that is creating peril, use the singular form; danger.
I also removed the preposition at the end of your sentence.

"which lay around" not "lied around".


"lay" and "lie" are confusing verbs in English and even English speakers get them mixed up. At the simplest level, "lay" is a transitive verb and requires an object so you can lay eggs,  lay bricks,  lay a blanket on the sand or lay a body in the ground. "Lie" is an intransitive verb so you lie down, lie on a bed etc. Problems arise with past tenses. The past tense of "lay" is "laid" but the past tense of "lie" is either "lain" or "lay" depending on context. "Lie" in the sense of telling untruths has the past tense "lied". 

If you have access to Fowler's "Modern English Usage" he gives an excellent explanation of the difference.

Your English ability continues to be severely lacking.

You don't need the comma and it should which lay around.