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Antagonists are not necessarily bad guys. They prevent your protagonist from achieving her goals.

Free yourself of the labels and write your characters true to themselves. What you seem to have in your protagonist is something of an antihero in that she has killed her entire family and anyone else who ventured near enough to reach her.

The reader need not fully identify with your protag - a young girl who kills is not the most endearing sort. Show why she does it.

You might find, as I did once, that my original hero turned out to be an inadvertent and unaware villain, flipping the man he thought of as the arch villain into the hero. I stopped thinking of them as good vs evil and saw that the purported villain was striving to preserve the world from the consequences of the actions of the hero. I just considered them by their names and the plot developed itself.

Readers having sympathy for a victim of your protag’s earlier evil is not a problem. One thing I wonder, you say she thought she was alone and the last human alive. Why then would she not have felt relieved to see other humans? Was she frightened? Did she think People! I am not the last. Wait, why are they here? No, can’t let them find mom and dad. Need to kill them and run.

If she killed them to cover up her earlier crime, she might be a bit too dark to engage the reader completely. The reader might be curious regarding what other havoc young Eris will wreak, but feeling as Eris feels might be a bit of a stretch.

Let them understand why Eris hates this good woman who stands in her way but don’t expect them to detest her too. They might see her as Eris’ only hope of redemption.

If your characters are engaging enough and fully realized, the reader will probably be intrigued.

The answer to this lies in (frustratingly) another question:

Why does your protagonist consider them "evil"?

If you can come up with something plausible and relatable for the answer to this you might just have a shot.

If the reason is due to a misunderstanding (or similar) on the protagonist's part (e.g. they believe the antagonist committed atrocity X when they didn't) then you can still do that so long as the reader has the same information that the protagonist does to lead them to that conclusion.

If they really are Lawfully Good in the classical sense and if your protagonist is more likely to be the one doing classically "Evil" behaviors then it's going to be a tough sell. You might be able to play into Anti-Hero status or make them likeable through other means such as making them super-charismatic, or funny etc and use the inertia of that built up appeal to encourage the reader to side with them over the antagonist but that's difficult, readers aren't idiots and if they see a character they like acting in a way they don't agree with you risk a backlash.

Can I keep my readers' loyalties with my protagonist, not my antagonist?

You can lead a reader by the nose a bit into being supportive of a particular character but ultimately they are going to sympathize with the character they find most sympathetic - which might not always be what you intended. There's nothing wrong with that, that's the joy of human nature.

As others have said, the antagonist doesn't necessarily have to be a bad guy. It's also worth mentioning however, that "bad guys" generally tend to think that what they're doing is good.

Consider for example someone who holds order and stability to be the most important thing there is, and so acts to stop any major change from happening, whether that change would be ultimately good or bad. What they're doing is upholding the order and stability that they hold dear, and they may well think they're truly doing the best thing for the country/world/etc. But what if this means they oppose getting rid of slavery, for example, because that is also a major change?

Consider also the ruler who is forced into a hard decision. They may be forced to choose between closing off all borders to protect their people from a plague that's ravaging the nearby countries, or sending aid to a long-time ally who has been struggling with the plague. Whichever decision they make, perfectly reasonable people can come to the conclusion that it was the wrong one.

Real-world problems are complex, and the best writing shows this. An antagonist whose motives and reasoning you can understand and perhaps even agree with is a sign of a good writer, in my opinion.

Some examples of this type of antagonist:

(the list below contains spoilers, I have listed author/publisher for each entry so hopefully you can choose what you want to see)

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  N.K. Jemisin's

  
  
  

  
  

  The Hundred Thousand Kingdoms

  
  

  
  


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  Brandon Sanderson's

  
  
  

  
  

  Mistborn trilogy

  
  

  
  


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  The Konami video game

  
  
  

  
  

  Suikoden 2

  
  

  
  

This can be done in a number of ways, though I admit it may be difficult to make a genuinely good leader a primary antagonist.

• Good guy is actually not so good. Your antagonist may be widely
  respected and acting selflessly for the good of the society, but
  there is a disturbing darkness in him. Think about Agent Smith,
  from the "Matrix", or High Sparrow in "Game of Thrones", or
  sheriff Will Teasle in "Rambo". In the end it is becoming clear
  that the good guy was clearly not so good.


• Good guy is acting in a mistaken belief that protagonist is a threat
  to the society. This is particularly common in Fugitive Arc (TV
  Tropes) stories, when we see a genuinely good law enforcement officer
  as an antagonist (but not the "big bad"), and still root for our
  protagonist, who is on the wrong side of the law.


• Comedy. Here the audience can root for the bad guys knowing that they
  are not really bad. Consider "Smokey" from "Smokey and the
  Bandit", Dean of Students Ed Rooney from "Ferris Bueller's Day
  Off" or concierge Hector from "Home alone 2".

The classic example of an effective Lawful Good antagonist is Inspector Javert, from Les Misérables. He is a good person who cares deeply about upholding the law, which brings him into conflict with the protagonist, Jean Valjean, multiple times throughout the story because Valjean is a reformed thief who had to break parole and assume a different identity in order to get a fair chance from society. Javert's main character flaw is that he (like so many other people in his society) doesn't truly believe that a person like Valjean is capable of reforming and becoming good.

Another example can be found in Marshal Samuel Gerard from the movie The Fugitive. His job is to hunt down the titular Fugitive, convicted murderer Dr. Kimble, who escaped on the way to death row. Unlike Valjean, who was legitimately a thief, Kimble was wrongfully convicted of murder, but Gerard doesn't particularly care when Kimble protests that he didn't do it because, as the saying goes, "that's what they all say." But unlike Javert, when solid evidence comes up that Kimble is innocent, Gerard is willing to reconsider and eventually turns to helping Kimble.

So yes, there are multiple ways to have a scenario with a Lawful Good antagonist acting against a good protagonist and still end up with a good story.

Two Lawful Good people can still end up violently opposed, they just need to have different views of reality, laws or good.

The classic scenario would be two soldiers who are both good, kind and thoughtful people but happen to be on opposite sides of a war. They can resent and hate each other because that's easier than hating the situation or their political leaders or anything else. It gives them something tangible to fight when they can say "that's the bad guy, this person is why my life is bad".

Your protagonist needs to have something likable about them to keep things engaged. Show the conflict from their point of view and try to bring the readers into that mindset and you can pull this off but it is tricky.

Very few people consider themselves to be "evil."

So, it would be very realistic to have two people who are good and even lawful oppose each other.

Think about two such people. They each have a goal that they think will make things better (or keep them from declining). They are committed to their respective goal. They will do anything that the law and their morality allows to achieve their goal. Now consider that their goals have mutually exclusive results or have unintended consequences that interferes with the other's goal.

They may be so invested in their own goal that they see any interference with it to be evil. Thus, you could have two good people who see each other as evil (or merely just wrong).

Politics is a good example of this.

Your story can only be better if both characters are good and oppose each other. If the readers sympathize with the antagonist, the protagonist's victory will be tinged with a bit of tragedy. If you really want to tug on the hear strings, in the end, let protagonist see that the antagonist is also good but must fail for what the protagonist sees as the greater good.

People are Complicated

And also compartmentalized. You can find a lot of examples in history of admirable, honest people with feet of clay. One very common twist for the scenario you’re spinning is that she really does put her own group of survivors first—but at the expense of others, and that’s why the hero has to fight them. Or perhaps she’s too loyal to her family or her own circle, who aren’t as noble as she is, and isn’t willing to restrain them. Maybe she has a tragic flaw.

Do We Need Another Hero?

Maybe she’s not “the villain,” just the worthy opponent of the main character. The two sides might be in an irresoluble conflict that she wishes were not necessary. You might be telling the story from the villain’s point of view, or there might be no villain at all.

It’s Not Her, it’s Them

The hero is fighting another group of survivors. Maybe the leader is a good person, but not all her followers are, and she just doesn’t know about them, or can’t stop them.

War! What is it Good for?

If the antagonist turns out to be a good person who doesn’t want to hurt the protagonists, everyone could realize that and stop fighting. The plot might even be about making peace and saving as many lives as possible. That’s a great happy ending.

The Federal Marshall in The Fugitive (starring Harrison Ford) is an example of a lawful yet dislikable antagonist. So yes, that kind of antagonist can definitely work.