I am quite sure that the painting's subject is Leonardo's mother Caterina in a distant memory. She died in 1495. Lisa del Giocondo's job was to be the model only.

At the time that Leonardo painted the portrait of his mother, whom he adored, she had already died. This is the reason why Leonardo chose the setting of the Holy Land, as he imagined it, as the background to the portrait. (The Jordan River is painted to her right and the Sea of the Galilee to her left). See: Cross and Yarn-Winder.

The idea is that she was alive in Leonardo's imagination.

This is similar to the background of Leonardo's paintings of the Virgin Mary, which also depict the same landscape of the Holy Land.

Thus, Leonardo glorifies the Mona Lisa as the Virgin Mary. See: Leonardo glorifies Salai as Saint John the Baptist.

Leonardo pictured his mother, who raised him until age five, in painting the Virgin Mary.

So, she was the only significant woman in Leonardo's life, hence deserved to be glorified as the Virgin Mary.

In all of his paintings, the Virgin Mary looks at her son. In this painting she looks at the painter.

The conclusion is that the painter is her son.

This would explain why Leonardo kept the portrait with him wherever he traveled, until his death.

This theory was suggested by Roni Kempler in 1976.