Since detailed support conversations were removed from Radiant Dawn, not much information on Leonardo's past is available in the game. However the released designer's notes help to shed more light on the subject.
The notes reveal that Leonardo is the son of a noble. Leonardo lost his father and older brother in The Mad King's War, and became an orphan as his mother soon followed them. After Daein's defeat in the war, the military school where Leonardo studied fell into the Begnion Occupational Army's hands. While everyone is being sent to the prison camps, he flees alongside a few colleagues. However, those colleagues are captured, one after another, and Leonardo ends up being the last remaining one. When he loses his way and is cornered by the Occupation Army, he is saved by a youth of his age. That was his first encounter with Edward, who would later become his best friend.