To some extent, yes. Medieval Just War theory, particularly that of Europe, was dominated by two specific traditions. First, that of the Bible, and especially Jesus' ideas on pacifism combined with Old Testament wars/conflicts.

Second was that of the Romans themselves, as your question implies.

I can go into more detail, but the two combine in interesting ways during the medieval period. For instance, you have early church father St. Ambrose writing a treatise called de Officiis, the same title as that written by Cicero a century or two earlier. Of course Origen is combining elements of early Christian thought with the Roman ideas of just war espoused by Cicero, but our get the point. Add to this the fact that for Western Europe, the Church was the main continuation of Roman jurisprudence (Canon law at the time owes much to roman law codes) and the two get very mixed.

Over the course of the medieval period we see these ideas mix and match in interesting ways. You also have a continual drive by some Christian thinkers to go back to the roots of Christian pacifism and non violence. I encourage you to take a look at Lateran II, John Wycliffe and others for an interesting look at how the establishment understood just war, and how those on the ideological fringe had sometimes very differing ideas.

Rao, H. Krishna. "JOHN WYCLIFFE." The Indian Journal of Political Science 3, no. 4 (1942)

Trigg, Joseph Wilson (1985). Origen: the Bible and Philosophy in the Third-Century Church

Fordham University - Medieval Sourcebook: Tenth Ecumenical Council: Lateran II 1139

H. Wace and P. Schaff, eds, A Select Library of Nicene and Post–Nicene Fathers of the Christian Church

If you are interested in the theory, I'd suggest you check out r/askphilosophy. They are probably more versed in the theoretical sides of just war