#2: Lily=best mom EVER
The second luckiest break comes when Voldemort can’t kill baby Harry. Now, I know this might seem a bit obvious, but it really can’t be overstated. The sacrificial protection counter charm Lily Potter places on Harry requires a number of specific things to occur in order to work. The simple fact that Voldemort is on a blood-thirsty rampage with his Death Eaters, and yet Harry is the only one protected by this powerful counter charm, tells us how rare this is. Heck, it doesn’t happen again in the whole book series despite a healthy splattering of magical murder.
Probably the luckiest part of the charm's success is how it required Lily’s sacrifice to be "pure." Meaning: she had to have a clear chance of survival in order for it to work. Snape’s love of Lily leads Voldemort to agree to spare Lily’s life, provided she doesn’t get in the way (spoiler alert: she does). Now, most of what we learn about Voldemort comes from other characters, but, to me at least, he doesn’t come across as the super reasonable sort. So for him to agree to spare a full-grown adversary, especially while planning to kill a baby in cold blood, seems a particularly lucky turn of events. At least, for Harry.