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This is for sure a duplicate question, but I'm sorry I'm just getting confused no matter how many articles I read. In the sentence,

And still they are not aware what powers lies between their hands!

Should this be lays, lies? And what should it be if the tense were changed to "were not aware"?

And still they are not aware what powers lie between their hands!

And still they were not aware what powers lay between their hands!

B1 [ I + adv/prep, L ]

present participle lying

past tense lay

past participle lain

If something lies in a particular place, position, or direction, it is
in that place, position, or direction

Lie (Cambridge)
Lie (Collins)
English verb: to lie

Present tense:
Singular: I lie, you lie, he/she/it lies.
Plural: we lie, you lie, they lie.

Past tense:
Singular: I lay, you lay, he/she/it lay.
Plural: we lay, you lay, they lay.

I agree with the other answers but, just to confuse you further, there's another possibility.

And still they are not aware what power lies between their hands!

This means that they have power between their hands but they are not aware of it.

And still they are not aware what power lays between their hands!

This means that 'power' is treated as an agent and it places something unspecified into their hands, i.e.

"And still they are not aware of the thing that power lays between their hands!"

So my answer is that both are possible but they mean different things.