This phrase is widely recognized and used to express accepting outcomes that are uncontrollable. I didn't get my preferred schedule, but it's the luck of the draw.
Pro Tip 2/3
Neutral Tone
The phrase is used neutrally, not to express happiness or unhappiness, just the randomness of life. I guess taking the last slice of pizza was just the luck of the draw.
Pro Tip 3/3
No Blame
Use it to indicate that a result is not due to anyone's fault or intention; it's random. The raffle winner is chosen by the luck of the draw, so don't be upset.