What is the basis for Lombard's view that the basis of justification for OT men was different than for OT women?

Full study: Medieval Readings of Romans

But of course, Lombard's view is based on the incorrect assumption that circumcision started with Abraham.

The practice of circumcision predates Judaism by more than 10.000 years. Circumcision is the world's oldest planned surgical procedure, suggested by anatomist and historian Grafton Elliot Smith to be over 15,000 years old, pre-dating recorded history.

The Semites most likely copied the practice from the Sumerians. Abraham is believed to have had circumcision performed on himself and on all male relatives and servants in his household whether of Semitic origin or not, as a mark of the covenant between his God and these people, known thereafter as His Chosen People, the Children of Israel. Historians date this as around 1800 BCE, clearly long after circumcision was introduced by the Sumerians and Semites.

So just as some have assumed that circumcision started with Abraham, so others like Herodotus have incorrectly suggested that the Children of Israel introduced it into Egypt during their captivity around 1200 BCE.

Evidence exists that ritual circumcision was being performed by the Egyptians as early as 2300 BCE, confirmation of this being a wall painting from Ankhmahor, Saqqarah, Egypt (dated in the eighth Dynasty, 2345–2182 BCE)

Now that we have established circumcision clearly predates Judaism, it is logical to search for the origin of this dualistic gender-based justification in customs that predate Judaism as well. Egyptian circumcision was used to demarcate a special elite class, very much like in the Abrahamic tradition, it is used to set apart the "chosen". Priests were the custodians of both secular and religious knowledge and they played a significant role in offering sacrifices to the Egyptian gods. Priests were expected to be pure morally and in physical appearance. The presence of the foreskin was regarded as a sign of female sexual organ and impurity and hence it was to be removed. As purity was a status of higher rank and a coveted attribute, the practice of circumcision, which originally was prescribed for the priests, ultimately became adapted by all men.

Priestesses in Ancient Egypt, on the other hand, were not circumcised and usually served in the temples of female deities. Those who served Isis were instructed to perform good deeds every day, such as anonymously donating to the poor. Detailed instructions for daily good deeds, rituals and sacrifices date back to the earliest dynasties.

In his commentary on the Sentences, answers six questions on circumcision: [1]

1. Its necessity
2. To whom it applied
3. Its requirements
4. Its efficacy
5. Its transformation through baptism
6. The remedy that preceded it.

It seems that the quote you cited does not inform the reader well about Peter Lombard's view on circumcision. He did not hold that circumcision and not faith & works justified men. But rather that men and women alike were so justified.

He says:

And yet there was one among those sacraments, namely circumcision, which conferred the same remedy against sin as baptism does now. [2]

So, circumcision being a sacrament of the Old Law, was made efficacious by faith, and thus the one being circumcised was still saved by faith.

Only Men: St. Thomas, arguing against the notion that women should have had circumcision (or some equivalent remedy), quotes Hugh of St. Victor in saying

the circumcision of the flesh was given to men alone, for the Sacred Scriptures customarily represented the soul by the masculine sex, but the flesh by the feminine, so that it would be manifest that circumcision conferred sanctification on souls, but did not remove the corruption of the flesh. [3]

Only Israelites because circumcision signified faith. But it was only the sons of Abraham who actually kept the faith, as all the rest fell into idolatry. Furthermore, Christ would be born of one nation, through Whom was there a future medicine, prefigured by circumcision. [4]

[1] https://aquinas.cc/la/en/~Sent.IV.D1.Q2

[2] Lombard, Sent. IV, 1.7.1.

[3] Aquinas, Sentences IV, D. 1 Q. 2 A. 2.2.SC

[4] Ibid, 1.SC