Well thanks everyone, I spent all night turning this over in my head. I play a paladin in my wife's D&D group, and little nuances and difficult decisions like this one are my favorite parts of that character. So apologies if I go overboard.
There is a lot of discussion in this thread about the ethics of what this paladin did, and ethics is a tricky topic. The concepts of good and evil, right and wrong can vary greatly across cultures. The ancient Vikings had very different ideas about valor and bravery and "a fair fight", etc., than the soldiers of Victorian England had. So if we want to argue about whether or not feeding an NPC to a dragon is right or wrong, I have good news: you're absolutely right, no matter which side you argue for.
But for this specific example, the title of this thread is "Paladin Just Committed Murder, What Should Happen Next?" So let's accept the fact that the DM has already decided that the paladin's actions amount to murder in this context...it's right there, in the title of the post. The paladin/warlock is guilty of murder in this game world, so let's start there.
Where I live, murder is a felony offense that is punishable by life in prison. In other states, it can get you the death penalty. So before we ever start worrying about the paladin losing his special powers, he might need to worry about facing charges for negligent homicide (assuming negligent homicide is a crime in this world. It could be like Skyrim, where you can slaughter dozens of people in a cave and nobody bats an eye.)
-----
This wasn't a "no-win situation" either, that others have suggested. In the original post, the DM had expected the paladin to challenge the dragon in a contest of wills, rather than combat, and the player lost the challenge. That loss should have consequences, or at least an impact...otherwise, the NPC's life meant nothing. And if the NPC was inconsequential, why was there even a contest in the first place?
This is a classic scene from fantasy literature, where the hero of the story must match wits with a powerful foe. Bilbo vs. Smaug. Odysseus vs. the Cyclops. It is a classic set-up for a hero, and this hero botched it: Bilbo gave the One Ring to Smaug to save his own neck, Odysseus got scared and fed his men to the Cyclops. >
sad trombone<
From the standpoint of the story, I feel there needs to be consequences for losing a contest of wills, just as there are consequences for losing a contest of battle. The nature of those consequences need to be discussed with (and agreed upon by) the player. Sure, the paladin didn't die as he might have in combat, but he certainly isn't a
winner here.
-----
And what is a paladin anyway? A lot of players choose paladin because they want to be a fighter who can cast spells, but they don't like the lack of damaging spells on the Eldritch Knight's list. So they choose paladin because it lets them do lots of melee damage, and handwave or ignore the roleplaying aspects and requirements. (Side note, Warlock is another problematic class for this same reason, and this character has levels of both. I don't envy the DM here.)
There's nothing wrong with this approach; play the game you like to play.
As for me, I think a paladin should be more than just a fighter with magic powers, and those powers should come at a price. The Player's Handbook agrees, and describes a paladin as "warriors that have turned from their former occupations to take up arms to fight evil." And their spells and powers aren't freely given; the paladin's oath is "a powerful bond, a source of power that turns a devout warrior into a blessed champion." It goes on, in several paragraphs, but this is already super-long.
I recognize that a lot of this stuff gets dismissed as "flavor text," and not played as hard-and-fast rules. So a lot of players end up frustrated when the DM reminds them that they have an obligation to their oath. (See also: reminding warlocks of their pact.)
Important note: It's fine if you want to play your paladin as a magical warrior and hand-wave the oath (or a warlock as a wizard and hand-wave the pact). All I'm saying is, the rules as-written won't back that argument.
So if the source of that paladin's power (his oath) was broken, he might be cut off from his powers until he can make things right. A mission to rescue or avenge the NPC might make for a cool side-quest. But we don't know what the paladin's oath was, so it might not even be an issue.
-----
Yikes, sorry this is so long. I'll wrap it up.
In conclusion, the paladin was presented with a classic fantasy trope (a battle of wits against a dragon) and failed, and consequences of that failure are appropriate. But without knowing more about the paladin's oath, and the rules of the game world, I can't make any recommendations on what should happen next.
Something should happen, though. Otherwise, what was the point?