You're dealing with a colleague — maybe a boss — who's made it clear they don't respect you, and you still have to work with them every day.
Lincoln's entire cabinet was, by design, full of men who had run against him for the Republican nomination and lost — several of whom thought they were more qualified for the presidency than he was, and said so. Historians call it his "team of rivals." He built it on purpose, knowing exactly how much friction it would create, because he wanted the strongest arguments in the room, not the most comfortable ones.
That's a genuinely different approach to a hostile colleague than most advice offers. The instinct is usually to minimize contact, or to win the person over, or to route around them entirely. Lincoln did something else: he kept them close, gave them real authority, and let the friction actually improve the decisions being made — while never losing track of who was actually in charge.
It cost him plenty of frustration. It also meant that when it mattered most, he had people around him who told him the truth instead of what he wanted to hear, because he'd never demanded their loyalty as a condition of the job.
If you're managing a difficult work relationship right now, ask him how he actually handled the day-to-day friction of it — not the history-book version, the practical one.