Oh come on, this is ridiculous. I mean from popular fiction, not history. I literally used Captain America as an example, and I can easily find a character that matches every class and works in D&D parties.
Ranger: Robin Hood
Fighter: Boromir
Paladin: Geralt of Rivea
Rogue: Arya
Barbarian: Conan
Wizard: Merlin
Druid: Radagast
Warlock: Melisandre
Couple of points.
Geralt of Rivea is a paladin? How? He doesn't heal, he certainly doesn't cure diseases and has zero religious overtones. Vengeance paladin maybe? Certainly not the archetype that most people go to for paladins.
Conan rages? Since when? Does he speak to animals or have any sort of totemic spiritual bent that I missed? Conan is nothing like a D&D barbarian. He's about as close to a fighter as you can get.
Merlin is most certainly not a D&D wizard. A 5e wizard is Harry Potter, not anything from fantasy written before about 1990.
These aren't even close.
But, for archetypes of warlord:
1. Cutter from Cook's Black Company series. Absolutely freaking perfect warlord and actually fits rather well as a lazy lord archetype as well.
2. Multiple characters from the Malazan Fallen series, particularly many of the marine characters.
3. Sam Vimes from Pratchett's Guards Guards series. Again, excellent example of a warlord in action.
4. Miles Vorkosigan from Lois McMaster Bujold's Vorkosigan series. Another very excellent example of a lazy lord archetype.
In this particular case, I'm legit curious. Because when I think of the Lazylord, I think of people like Sun Tzu, Cortez, Attila the Hun. People who, at the pinnacle of their ability, were not personally getting involved in fights.
The Lazylord just doesn't seem to fit the classic D&D gameplay of 6 people fighting a group of monsters/people. But I'm willing to believe I'm wrong on this, so I'm trying to think of a figure in history or fiction of someone in a small group going on adventures, who is using tactics to tell his comrades the best way to fight without personally getting involved.
Closest thing I can think of is Fire Emblem, but in even those the game gives you a PC who is a combatant itself.
Now, the thing to remember is that lazy lord was never actually a class. So, to be honest, for me anyway, if a 5e warlord precluded a lazy lord, I wouldn't have a problem to be honest. It never was a class, so, meh, it's not a hill I will die on.
But, in classic D&D style, the warlord works fantastically well. Take it from those who actually saw it in play, instead of listening to those who simply read the books and then brushed it off. It really does work excellently. It's a class that requires the player to pay attention to the game and also works to draw in the attention of all the other players as well. Think about it, in most D&D games, when it's not your turn in combat, there is generally nothing you can do. Sure, you might get a reaction, once in a while, but, by and large, after your turn is done, if you got up, left the table, and then came back before the beginning of your next turn, it wouldn't matter.
The warlord completely changes that dynamic. Anyone can now be called on to take actions outside of their turn at any time. Sure, it might just be movement - warlords could grant the entire group movement off turn, for example, or an extra saving throw, or an extra attack, but, the point was, you were being granted extra actions on a regular basis. It is such a fantastic class for focusing the group on the game to a degree that you don't see otherwise.
A lazy lord or a warlord, doesn't really matter, does that. It makes every round actually matter. You can't take your turn and then go back to playing Candy Crush on your phone.
THAT'S what a warlord brings to the table.