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There is almost never just one antagonist in a story. There may be a chief antagonist, a person who is directly working against the protagonist, but most stories are not actually like that, and even in the ones that are, there is more than one force, more than one person, whose actions frustrate the protagonist's goals. Some of those forces may lie within the protagonist themselves. 

Not only may some of those antagonists be morally good, I would suggest that some of them have to be. After all, what forces prevent the protagonist from achieving their goals? Some are the evil forces they are striving against. But some of them are the moral constraints that the protagonist works under. If the protagonist was unconstrained by any moral consideration, they could throw any force, and weapon, any stratagem against the principal antagonist without constraint. That would make it much easier to win. But it would make for a much less interesting story. The constraints of the moral law on the actions of the hero create the kind of moral dilemma that is a central feature of the plot of many stories. 

So yes, not only may an antagonist be lawful good, it is very close to being an iron role that some antagonists at least must be lawful and good or there will be no story. In some cases, the principle antagonist may be lawful and good. Nor does this mean that the protagonist must be evil. Sometimes it is entirely appropriate the the protagonist loses in their quest, though they may gain something other than what they were seeking. This is often the shape of the maturation plot, for instance. 

The QB loses the big game but gains the respect of the dorky-but-hot girl with the adorable younger brother that the best receiver on the team is bullying. QB exposes the bully, who is benched, thus causing the team to lose the championship game. Hero loses, but really wins. The main antagonist here is not the bully, it is the dorky-but-hot girl who is, of course, the sum of all virtues, and who turns down the QB's advances, until the tearful scene at the <airport, train station, laundromat, library> where she learns of his heroism and ... well, you've seen the movie. 

The moral order itself is an antagonist in most stories, constraining the ways in which the protagonist pursues their goals, perhaps even to the extent of preventing them from achieving those goals. The US targeting of Qasem Soleimani is a case in point. No one weeps for Soleimani, but there is great debate over whether killing this very bad man was a violation of the moral constraints under which the US should have acted. The moral code constrains how good people prosecute their struggle against bad people. Thus it is an antagonist in their stories.