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Neither of them had any idea what would lie ahead if they decided to press on. (would lie ahead)

I don't see any errors. If I wanted to be really picky, I'd suggest replacing "would" with "might." I think that would read a little better. But there are no actual mistakes.

The sentence sounds right as it is to me. I don't find any error.

If you're asking whether it should be "would lay ahead," the answer is no. If we were to remove the word "would," then "Neither of them had any idea what lay ahead" would be correct as a factual statement (i.e. something was ahead and they did not know); but when we add uncertainty (i.e. there might have been something ahead, but they didn't know) through the use of the conditional "if" and the auxiliary verb "would," the correct verb is "lie."

I don't see any errors here and I couldn't find anything online to suggest that it is wrong.

DURGA P T M wrote: ↑30 Jun 2021, 10:59 Neither of them had any idea what would lie ahead if they decided to press on. (would lie ahead)

Not to my knowledge, no.

I think you need a preposition after "idea". try to put some.