. It's the suffering of the Lake-town residents at Smaug's hand that initially awakens the feelings he has buried so deep. But I'd love for Bilbo to be the catalyst for the significant change of heart he later undergoes--his transformation if you will.
It's Bilbo, our titular hero, who reminds Thranduil what's important in life. And it's Thranduil's actions towards the Lake-towners and prior to the battle that inspire Bilbo to fight with the elves. Plus I like to think that Bilbo, like us, saw the King's true nature buried beneath the despair and fear during his stay in Thranduil's halls. (That's partially why I was so upset they failed to show more of him scampering around looking for an escape route, pilfering food, and observing the elves--namely the feast which is one example of Thranduil trying to do right by his people despite the darkness slowly enveloping their lands.) It's Bilbo's simple nature and honesty that brings this out in Thranduil. We need Thranduil to be perceived as a cold, arrogant, selfish King for this to come across; we need that sharp contrast. Think about it: this strange little creature brings the Arkenstone, this most coveted gem, and presents it to Bard and Thranduil to save Thorin from himself.
It's such a selfless act. Bilbo cares nothing for treasure but instead is acting out of friendship and honor. That is epic! Thranduil, the great Elvenking, is taken aback at the integrity and heart in this seemingly insignificant creature. (His dialogue from the book is fitting.)
So in conclusion, I'll have no problem believing Thranduil's kindness towards the Lake-towners and Bilbo as genuine in TABA. Imagine you haven't left your home for many years and when you do, you're confronted with the horrors of a dragon attack and the suffering of many innocents. Imagine the inner turmoil that would cause and how it would impact you--the memories it would invoke. But then you witness such selflessness and kindness from an unlikely creature. That's essentially what happens to Thranduil.