At one point, you decided that you wanted to give Lawful Good a chance. Everyone said you’re basically signing up to be the most frustrating person in the Dungeons and Dragons party, but you think that it would be fun to play the game with a strong sense of morality instead of just being some murder hobo in search of a paycheck. You even decide to go to the extreme end of the spectrum so there are consequences if you fail to stick to the morals you’ve chosen. Everyone jokes about the stick insertion that comes with your first level of Paladin, but you think you’ve clever enough to play to the nuanced alignment of Good over Lawful. So you roll up your character, assign yourself the role of the party’s moral compass, and then discover that you’re the main impetus behind the party’s decisions and everything you know is at odds with how you are choosing to play your character.
You manage to discourage the rogue from poisoning the well of a village you suspect has been behind the attacks on your colony, only to be found out anyway when your bluff is called and the Yuan-Ti (snake person) you’re talking to is actually a dragon posing as a god. You also manage to stay standing in a later encounter when everyone else falls only to lose your arm as you take all your hit points in damage from a single hit because the rogue got you into an encounter you couldn’t win. Later you stay out of the rogue’s business so they can do some clandestine research in the undercity, but they wind up wasting a lot of time and money because they go about doing things the most back-asswards way possible because they forget that other people can make sense motive checks and only survived because they got lucky, all while you take down what turns out to be a lich who is directing an attack against the city you’ve stopped in. A while later, you lose your cool and your fancy Paladin powers because you lost your temper interrogating the assassin who killed your friend and then told you not to take it so personally since he’s just a contract killer. Later, once you’ve atoned and aligned yourself with a god who not only helped you out in a pinch earlier but has a more proactive view on punishing evildoers, you sacrifice your life to buy the party time because the rogue accidentally woke an ancient proto-lich and even then only two members of the party survive because the Scout decided that keeping the proto-lich in the tomb was worth more than his life.
Finally, you’ve alive again, you’ve worked things out with the party so they respect your authority a little more, and things are finally starting to go well aside from the rogue who has a bit of a penchant for questionable decisions. One of which was to reveal your party’s goal to the prisoner you were interrogating and now you can’t just let this goblin cleric walk away to report back to his superiors. If the rogue had the stones or the sense, he’d “let the cleric go” by taking him over a hill, killing him, and hiding him in portable hole or bag of holding until a more permanent means of disposal became available. But you know the rogue isn’t going to do that and you can’t exactly tell him to because you’re supposed to be playing the moral compass of the party and there’s little point to doing that if you’re telling everyone how to get around you.
In this case, it seems like your options are extremely limited because all you can do is either keep him prisoner or let him go. Fortunately for you, there are actually a larger number of options open to you than you realize. For a complete description of alignments, check out this great video by Matthew Colville, but the thing you need to know is that the best definition of “Lawful” is that you believe society benefits from having laws and that the laws should be followed. “Good” is usually defined as “not evil” or, more usefully, as being willing to grant people the benefit of the doubt when they ask for or look like they need help. You can also see this particular comic page (specifically the last panel) from Tarol Hunt’s “Goblins” for the best definition I’ve found. This means that, as a Paladin, all you really need to do is believe in the usefulness of laws, support those laws to the best of your ability, and that you’re willing to give people assistance without needing proof.
This allows you some leeway depending on the world you play in. In some particularly religious game worlds, Paladins are allowed to act as executioners or judges. There’s even a whole prestige class in the three-point-five edition of D&D specifically for this available to certain divine casters (Paladins and Clerics, mostly). In that case, the Paladin could put the prisoner on trial and either permanently lock them up or execute them, if they’re found guilty of particularly heinous evil. Depending on the which religious order of Paladins your character belongs to, the idea of a trial by combat is a fairly typical way to resolve problems like evil prisoners. Especially for Paladin orders that are a little more focused on purging evil. Hell, if you’re a really anti-evil paladin, a simple “detect evil” is enough. Dungeons and Dragons has objective Good and objective Evil for a reason. The definition Tarol Hunt supplies is actually a really great way to cut through the potential subjectivity involved in defining good and evil so it still fits into a “yes or no” system like Dungeons and Dragons.
While a lot of this post (pretty much everything up to this point, honestly) is geared toward the Paladin in the party of my campaign, it’s honestly a problem I see a lot of Lawful Good characters run into. Sometimes it feels either like you need to resign yourself to having a stick up your character’s ass or wind up basically murdering everything evil just because it’s Evil. Really, though, you have more options than this basic dichotomy. A lot of it depends on the laws of the land and what has happened in the campaign you’re playing in (for instance, some particularly lawful characters might be granted the power to enforce the laws of the land as a part of acting on behalf of a ruler), but you always have options. If you’re not a Paladin but some other class and still Lawful Good, perhaps a Knight or a bounty-hunting Ranger, you still have essentially the same options. Lock them up while you drag them back home, find a way to control them using magic, invest in a jail wagon of some kind, hire people to hold onto the criminals you capture, win them over to your side by giving them Stockholm Syndrome, cutting off their legs and them giving them first aid so they can’t run away but also don’t die, killing them outright, a trial by combat, or just letting them go.
All that being said, it is so much easier when you’ve got some chaotic or neutral characters who are a little more willing to DISCREETLY dispose of an inconvenient prisoner without tipping off your character. That requires a certain type of player, though, and unfortunately for you, you chose to be a Paladin who can’t even suggest such a thing without running the risk of losing their divine powers. At least Knights (one of the only other classes with a Lawful alignment requirement) can act unlawfully without permanently losing everything unless they do it enough to change their alignment.
Like all things in Dungeons and Dragons, the sky is the limit. Ask questions, try to puzzle it out, spend some time considering how your character defines “Good” and “Lawful.” There are more options than you realize and Lawful Good doesn’t mean your hands are shackled when it comes to dealing with moral inconveniences.