Obviously the whole movie is based around this, but there is a moment just after the first battle in Rome, Maximus discards his sword and picks up a spear on horseback. Did he plan to throw the spear at Commodus in the audience? He then discards the spear for the arrowtip.
I think he was going to TRY to spear him if he got a clean shot, but one never eventuated, so he dropped the spear, then (as the other poster said) he picked up the arrow tip in the hope of killing him, but didn't want to do so in front of a little boy. From the real perspective the boy would have historically seen loads worse, but it's made from a modern perspective *shrug*
Have you read much Roman histories? He (at his age) would probably already be scheming how to manipulate himself into power over the corpse of his uncle. He probably would have started to befriend (or at least seek alliances) with various Praetors for when the tine was ripe. There is no way he would have been as innocent as a 20th century lad who Lucius was portrayed as.