You can understand it like this:
Lay = existing, waiting
Ahead = in front of you, on the road.
It means something is waiting there for you and you will reach it soon.
We never say "(someone) lays something ahead", we say "something lays ahead (for someone)".
It always means something like: "someone is going to encounter this thing"
"Trouble lies ahead for drivers on the mountain road, because a snowstorm is coming"
Often used metaphorically:
"Big problems lay ahead for Europe, the economic situation is getting worse"