Josh, your DNA testing company won't be able to determine that accurately since they have been known for false positives as well as false negatives when it come to companies predicting Sephardic Jewish ancestry.
As I always say, the best approach is to upload your DNA from whatever company you used to GEDmatch and Family Tree DNA in order to manually browse or search for Portuguese, Spanish, and Latin American Catholic matches deep down in your list, then to see if they cluster on particular chromosome numbers and particular areas of those chromosomes in your Chromosome Browsers, then take it from there. There are verification processes that should be undertaken to make sure bad data isn't causing identical-by-chance matching. If you had Eastern Ashkenazic ancestors you are nearly guaranteed to have at least one Sephardic ancestor who can be found genetically.
Susan, plenty of data have been collected by this point but relying on imperfect calculators to have something show up is problematic. A barrier is most of the surviving Sephardic populations aren't purely Sephardic. For instance, Moroccan Jews have varying degrees of indigenous Berber admixture (although Spanish-speaking Jews from northern Morocco have less of that), while Turkish Jews and Bulgarian Jews have large degrees of admixture with Ashkenazic and Romaniote Jews, and Sephardim in Aleppo, Syria mixed with Middle Eastern Jews. Matching a modern Sephardic person or having genes similar to a modern Sephardic reference group does not prove Sephardic descent.
Kenneth said it's "a matter... also of Italians having Jewish DNA". Yes, some Italians have Jewish ancestry, in some cases as recently as the 1400s-1500s. It's particularly apparent among Sicilians living in the Siracusa region (SE Sicily), the province of Agrigento (SW Sicily), and the Palermo region (NW Sicily). Sometimes their Jewish ancestry is Sephardic Jewish in origin, other times from the pre-1492 population of local Jews of Romaniote or Italki extraction whom I've been calling Sicilian Jewish. Segment match analysis turned up these connections.
Also there have been some documentary clues. Searching Sephardic SIG's archives here, I saw Nardo Bonomi mentioned in message #612299 the Inquisition case of a Jew-turned-Catholic in Agrigento in 1535 named Jorlando La Licata.
Then I saw another confirmation of the genetic matching pattern I witnessed in Nardo's message #319899 that indicated members of the Palumbo family lived in Sicily in the 1500s and the Inquisition went after them, too. Nardo says one of their cities was Palermo. In message #612203 Jan Meisels Allen referred to 5,000 or more Jews in Palermo who were forced to pretend to be Catholics.
Then there's message #611131 where Michael Waas referenced an apparent Jew named Josue Rubi who lived in the city of Siracusa in, he thinks, the late 1400s.
Hence providing explanations for the existence of Jewish DNA in precisely those same places: Agrigento, Palermo, and Siracusa. Just as Jewish DNA exists in other regions (e.g., Mexico, Spain) where the Inquisition persecuted people and is findable by using my techniques to locate cousin matches between Jews and Catholics.
I don't know whether there's Jewish DNA to be found among residents of towns in the province of Messina (NE Sicily), such as those in Susan's family. Sicily is pretty diverse with regional DNA differences.
My take on the DNA segments I found shared by Sicilian Catholics and Ashkenazic Jews, which are not common, is that one of the Sicilian Converso men escaped to the east then he or a child went northeast. It's documented that there were some Jews from other parts of Italy who made it to Poland. In Alexander Beider's "A Dictionary of Jewish Surnames from the Kingdom of Poland", he mentioned that Moses Montalto of Lublin (d. 1637) had a surname indicating his family's origin in the Italian town of Montalto. He also references Chaim Felix Vitalis, who studied in the city of Padua before he moved to Poland, and to Rabbi Abraham Italicus of Poland.
Susan's ancestors from Lvov and Skalat probably had some Sephardic in them because Lvov was one of the first destinations for Sephardim arriving in the Polish realm from Turkey and spread out over Galitzia after that.
Kevin Alan Brook
author of the 5-part series on Sephardic ancestry in Yiddishland for ZichronNote (SFBAJGS