When the Aruch translates a word to "La'az" which language is he using? Being that he's from Italy, is it Italian? Or was Latin still in use then?
The introduction to the 3-volume HeArukh al HaShas (edited by מאיר מיזליש) includes this in its introduction (page כ):
כאשר מזכיר הרב שפת לע״ז — כוונתו לאיטלקית שבזמנו.
When the author mentions the language לע״ז — the intention is to Italian of his time.
Similarly, the 7-volume Arukh HaShalem (edited by חנוך יהודה קאָהוט) writes:
הלועזים ר״ל העתקות מל׳ איטלקית אשר היא היתה שפת ארצו ואותה ידע בתכלית השלמות.
The foreign words, meaning translations into Italian, which was the language of his locale, and which he knew fluently.
This would not be modern standard Italian, which developed later (R. Nathan b. Yeḥiel lived in the 11th century).
According to Luisa Cuomo in her doctoral dissertation on the Arukh's Italian glosses, Le glossi volgari dell' 'Arukh di R. Nathan ben. Jechi'el da Roma, vol. 2, [Hebrew translation of the Italian introduction in vol. 1], p. 11:
"...the main phonetic traits point to a dialect that is mainly of central Italy (north-central Abruzzo, Sabina, Marche, east-central Umbria) with a strong emphasis northwards to the area of the border between Tuscany-Umbria and Lazio. This dialect is significantly different from the one spoken in Rome 150 years later."