Disclaimer: The usual disclaimers that I do not own Harry Potter or any of the characters. This is just for fun.
The prophecy came just in time for Lily to act. Within hours of Albus visited the Potter residence with an unusually sombre expression and breaking the news to them, Lily made an urgent appointment with the Potters' private healer and asked what options the Wizarding world had about inducing labour early, even just by a few days. She met a stone wall. Unless she or her child were in medical danger, they would do no such thing; she and her unborn baby were almost obnoxiously healthy.
With a morally grey area application of spells and memory charms Lily tracked down a muggle midwife who said much the same thing, perhaps with just a little more sympathy than her magical counterpart. Although the woman could not approve a medically induced labour, she did take pity thinking Mrs Potter merely uncomfortable in the late stages of pregnancy and offered a list of old wives' tales she could safely try at home at this stage.
Ever the noble Gryffindor, Lily flooed Alice to fill her in on the details. Theirs were the only known children that could fall prey to the prophecy, but if they could birth their babies before the end of the month, they would be safe. Alice may have followed through had Lady Longbottom not interfered. Frank reluctantly sided with his formidable mother and the two purebloods convinced Alice not to go through with her muggleborn friends' suggestion, proclaiming it cowardly and dangerous. Afterall, a baby is born when they are ready and not a moment sooner.
So it was that Lily replaced her pumpkin juice with pineapple, drank concoctions of raspberry leaf tea instead of her usual Earl Grey, gulped down food spicy enough to send James running from the room with his eyes watering, and was more active at night than ever before.
Her dedication and heartburn paid off, and that on 29th July 1980 Harry Potter was born a healthy 8lb 7 oz with a shock of black hair, greeting the sunrise with his squalling protests. Neville Longbottom was born the following day.
No longer the target of prophecy, the Potters lived to give Harry a little sister 2 years later and see their children grow. The Longbottom's went into hiding under the Fidelius; both saving and condemning them. Alice and Frank would not be tortured into insanity, but they would live having to look over their shoulders while raising their son for almost certain death. Alice never forgave Augusta for talking her and Frank out of Lily's advice.