I've been a big fan of the Goths for a while now, having played as the Ostrogothic Kingdom in TW: Attila's The Last Roman Expedition on 3 occasions, as well as motivated by my tendency to advocate for the loser in many conflicts all across history. I also definitely agree that the Gothic War is underrated on this site, and deserves more recognition.
In my opinion, the best opportunity for an Ostrogoth success is as early as possible in the war, during the Siege of Naples in 536, and here's why.
At the Siege of Naples, Belisarius had only 8000 men; he would have 10600 at Rome the next year, so not a big difference in numbers for him, but hey, its something.
Furthermore, unlike with Rome, which immediately accepted Justinian's rule, the citizens of Naples decided to resist Belisarius, and formed a militia to fight alongside 800 Gothic soldiers. Now, Naples did eventually fall, but in large part due to the failure of the Gothic king, Theodahad, to come to the assistance of the city in time, leading to his overthrow by Vitiges. Belisarius would later go on to defeat Vitiges in the Siege of Rome due to having the support of the Roman citizens and thus the ability to quarter his army behind the protective walls of the city of Rome; in an alternate world where Theodahad does come to Naples, Belisarius would not have this liberty. At Rome, Vitiges did have 25000-45000 men which Theodahad would likely also have at Naples, thus Belisarius would not only be heavily outnumbered but would be out in the open to Gothic attack as well.
Now, we all know he could just pull off another spectacular victory like the Battle of Dara or Ad Decimum, but this is alternate history guys, we're not just going to make some small change to the world only to get the same end result. For the sake of the POD, Belisarius loses, and is killed in battle. Whether Narses also lands in 538 is up for you to decide, but lets say he does; in my opinion, given his measly force of 7000 men, which was intended only as reinforcements, he would lose, but potentially this untested commander is given an actual force, do you think he wins or loses?
Another POD would be not having Theoderic the Great's heir, Eutharic, die in 522 and let him live on to inherit the dual Gothic thrones. Sure, Eutharic would be an old man, aorund 65 when Belisarius invades, but the combined power of both Italy and Spain resisting Belisarius' advance could be decisive, and the presence of numerous Ostrogothic kings including the great Totila after Theodahad's death showed that there was no shortage of Gothic commanders to help him fight, and I feel there is great potential for Totila's name to still rise into the annals of history in the case of such a conflict, distinguishing himself in battle.
Alright, so those are my two PODs for a surviving Gothic Italy that has also managed to save its population of 7 million from being cut down to 2.5 by the constant fighting and Justinian's Plague.
P.S. On the topic of the Lombards, I feel that, if not convinced to ally with the Ostrogoths, that they would be easily repulsed from Italy in this situation. The primary reason they had been successful in their Italian campaign IS because the constant fighting between Greek and Goth had severely depopulated the region, and with a strong Ostrogothic state, I find it unlikely for them to successfully break through into Italy.
P.S.S. Another POD could merely be Belisarius dying at Dara or Ad Decimum, the former buffing the Sassanids significantly and the latter preserving the independence of the Vandals (depending on your view, Belisarius' death at Dara may also prevent plans for a Byzantine reconquest for the time being as well).