According to Catholicism, does the Old Law justify? Or is Christ, faith, and the New Law necessary to justify even those who lived before Christ?
Those who lived before Christ waited for Christ in "Abraham's Bosom"—also called the "Limbo of hell or of the Patriarchs" (limbus inferni seu patrum), and Christ conducted them to heaven at His Ascension.
The Council of Trent was convened in order to combat the errors and heresies of Protestantism. The Council's Sixth Session (13 Jan. 1547) was on justification. It affirms that not even the Old Law could justify (ch. 1):
The holy Synod declares first, that, for the correct and sound understanding of the doctrine of Justification, it is necessary that each one recognize and confess, that, whereas all men had lost their innocence in the prevarication of Adam,—having become unclean [Isa. lxiv. 6] and as the apostle says, by nature children of wrath, [Ephes. ii. 3] as (this Synod) has set forth in the decree on original sin,—they were so far the servants of sin, [Rom. vi. 17, 20] and under the power of the devil and of death, that not the Gentiles only by the force of nature, but not even the Jews by the very letter itself of the law of Moses, were able to be liberated, or to arise, therefrom; although freewill, attenuated as it was in its powers, and bent down, was by no means extinguished in them.
but Christ is necessary (ch. 2):
Whence it came to pass, that the heavenly Father, the Father of mercies, and the God of all comfort, [2Cor. i. 3.] when that blessed fullness of the time was come, [Gal. iv. 4] sent unto men, Jesus Christ, his own Son—who had been, both before the Law, and during the time of the Law, to many of the holy fathers announced and promised—that he might both redeem the Jews who were under the Law, [Gal. v. 4] and that the Gentiles, who followed not after justice, might attain to justice, [Rom. ix. 30] and that all men might receive the adoption of sons. Him God hath proposed as a propitiator, through faith in his blood, [Rom. iii. 25] for our sins, and not for our sins only, but also for those of the whole world. [1 John ii. 2.]
The Council of Trent in this session famously condemns Protestants' sola fide ("faith only") teaching on justification:
CANON IX.—If any one saith, that by faith alone the impious is justified, in such wise as to mean, that nothing else is required to cooperate in order to the obtaining the grace of Justification, and that it is not in any way necessary, that he be prepared and disposed by the movement of his own will: let him be anathema.
Thus, the Old Law did not justify.
We are told in Hebrews 11 and James 2 that those who lived under the Old Covenant, and even before the Old Covenant was given, were justified by their faith. Their faith was, and ours still is today, made alive and perfected in their works. James 2:24 says we are "justified by our works, not by faith alone."
They were responsible to live by the commands they had received at the time, but it is the Blood of Jesus that passes from the Cross back through all of history, and forward to all of the future, to cleanse the sins of all who obey, and live faithfully (Heb 9:11-28).