Justice is part of a moral framework. Law is part of a procedural framework. You can structure the law to try to optimize for justice, but the law has never been about morality, the law is about keeping society operating on top of whatever structure is dominant.

Example: the Supreme Court ruled in Ozawa v. United States in 1922 that a Japanese descended person could not naturalize as a US citizen despite having white skin because he was not technically Caucasian. The next year in 1923 they ruled in United States v. Bhagat Singh Thind that an Indian descended man could not natural despite being Caucasian because his skin was not white.

Why did the court give two contradictory reasons for the rulings which would each be negated if the reasoning were swapped? I wouldn't say it was for justice. It was because America at that time did not want non-white immigrants, and what 'white' is, is a fiction that means something completely different than what it claims to mean, and the justices were upholding that structure.