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On what basis do you claim that Greek was the "Lingua Franca" of the Roman Empire?? Latin was. The ruling class was Roman and the Romans spoke Latin and they made every effort to assure that subject people knew that language. All official documents were written in Latin - everywhere.

In some instances, as in the eastern part of the Empire, some official documents, like the inscription over Christ on the Cross, may have been written in Greek, but that inscription was also written in Latin and Hebrew or Aramaic - I can't remember which.

Probably, as an educated Roman, Pilot also spoke Greek, but I doubt his soldiers did. As I said, commands in the Roman Army were given in Latin, the men understood it, the officers understood it, even though they may have also understood their native Language like Thracian, Gaulish, or Celt-Iberian.

The educated Jews may have known Greek and Latin as well as Aramaic and Hebrew, but I doubt of the average Jew knew anything but Aramaic and possibly Hebrew.