William Miller summarized Jacopo's motivation as a semi-autonomous ruler was to favor Genoese interests when they conflicted with Venetian ones, but to cooperate with both when they showed signs of uniting against his neighbors, the Ottomans. For example, he aided Centurione II Zaccaria, Prince of Achaea against the Tocchi of Cephalonia and Zante.
Jacopo was married to Bona Grimaldi. Only one child is known:
- A daughter. Married to Nicholas Crispo, Lord of Syros. He was a son of Francesco I Crispo of the Duchy of the Archipelago.
Niccolò mentioned Jacopo as his father-in-law in his correspondence from the year 1426. However the name of his wife remains unknown. Niccolò had eleven children but no record exists of their mother or mothers.
An account by Caterino Zeno dated to 1474 names Niccolò as married to an otherwise unknown Valenza, sister of Theodora Megali Komnene, daughter of John IV of Trebizond. Whether this means Niccolò took a second wife or whether Zeno was in error has been debated by genealogists.
- Miller, "The Gattilusj of Lesbos (1355–1462)", Byzantinische Zeitschrift 22 (1913), p. 418
- Miller, "The Gattilusj", p. 419
- Discussed in Michel Kuršanskis, "La descendance d'Alexis IV, empereur de Trébizonde. Contribution à la prosopographie des Grands Comnènes", Revue des études byzantines, 37 (1979), pp. 239-247. Kuršanskis has argued that Valenza was actually a native of an Italian city, or did not exist at all.