Well, we're talking 5e, so there's a LOT of leeway here. The biggest clues are to be found in your deity choice.
Paladins are by the rules no longer bound to lawful good alignment. However, they are bound by a code of order for their philosophy or deity. Bahamut is typically portrayed as a good of the Greater Good, but one who also promotes the virtues of the Draconid peoples. This needs to be tempered through the type of paladin you plan to play when you hit the correct level, whether a paladin of devotion, or of Vengeance. (I think the Ancients paladin might be too incongruous for Bahamut). If you are taking the "vengeance" route and are playing a Vengeance Paladin, it still should be tempered by Bahamut's teachings, and each being, no matter race, should receive compassion if innocent.
But let's up the ante. You find one of the raiders from the original raid, lay dying by the wayside, if you don't intervene. A Paladin of Vengeance might slay him outright, giving him still more mercy than he gave his victims. He might even leave him there to die, as Just punishment to die just as his victims died bleeding out.
Were he a Neutral Paladin, he might even take the Dragonborn raider's water supplies and pour it on the ground in front of him, if he were similarly cruel to his victims before they died, though that knocks on the door of Evil and asks for a subscription to its newsletter...
If a Devotion Paladin came upon the dying dragonborn merc who helped raid his village, he might well heal the merc and find him shelter, but take him to a council for justice or ask guidance from his god on true justice, if civilization were not available.
Remember the final takeaway that a paladin fights evil, still - and standing in judgment of someone for their skin rather than their actions is still unjust and evil. It's just that their methods have more leeway than merely what lawful good will typically mete out.
