The phrase implies that the result is beyond human control and left to fate or destiny. We've done our best to prepare for the competition; whether we win is in the lap of the gods now.
Pro Tip 2/3
Beyond Influence
It expresses a situation where no further action can affect the outcome. After the interview, my job prospects were in the lap of the gods.
Pro Tip 3/3
Not Literal
This idiom does not refer to a physical location, but rather an abstract concept of fate. With the final dice roll, my entire fortune was in the lap of the gods.