Whatever details of history led to the apparent annexation and dissolution of Abilene in 32 AD, the fact of it probably had at least one small impact on the New Testament Story. The event must have served as one more reminder to Herod Antipas that Rome was always prepared to seize direct control over eastern territory, whenever conditions were right. In fact, Antipas already knew this very well, because Rome had claimed three other kingdoms in Syria's orbit since their failure to control Armenia after 2 AD. (The Empire annexed Judea in 6 AD and Cappadocia & Commagene in 18 AD.) Granted, Abilene was not a major territory, but neither was Galilee, relatively speaking. Therefore, even though the end of Lysanias' Tetrarchy was a minor event in history, it had greater significance to Herod as part of the larger pattern.
In short, Abilene reminded Antipas (age 53 in 32 AD) how important it was to govern well, maintaining local & regional stability. Ironically, this reminder came one year after the trouble of 31 AD, when the executions of John the Baptist and Aelius Sejanus had already left Herod with a bit more local unrest [not to mention much more personal uncertainty] than usual. And that unfortunate timing, in turn, makes the memory even more likely to have lingered, in some sense, until Good Friday, April 3rd, 33 AD. To say the very least - but emphatically, given the context - Herod's fairly recent thoughts about the former tetrarchy of Lysanias could not have diminished his cautiousness that morning in deciding what to do with Jesus.
In other words, while Herod Antipas certainly had many good reasons for smartly declining Pilate's offer of jurisdiction over the controversial, potentially insurrection-sparking trial of Jesus Christ, one of those reasons, perhaps not the absolute least, was the recent loss of Abilene.