It’s not necessariy the Gospel of Luke. A passage from Scripture is read at the start of each audience (Italian, English, French, German and Spanish). The Holy Father derives his catechesis from that particular reading and applies it to the topic at hand. Right now, his catechesis centers on the Church Fathers.
Towards the end of the Catechesis, priests representing the English-language, French-language, Portuguese-language, Spanish-language, German-languge and Italian-language speaking pilgrims greet the Holy Father in their name. After each greeting, the Holy Father reads a synopsis of the catechesis he delivered in Italian (except for the Italians, he simply greets them with affection). After this, he leads the faithful in the chanting of the Our Father in Latin (the words are printed in the back of the pilgrim’s ticket). Then he gives his blessing, which he extends to the pilgrims’ families and those who are at home infirmed.
No, I’ve never been to Rome, but, sometimes, when I can’t sleep on a given early hour Wednesday morning, I manage to catch the live broadcast of the papal audience on EWTN. It’s as close to the real thing as I’ll get.