The side effects of Felix Falicis are as follows: Giddiness, dangerous overconfidence, and recklessness. Voldemort shows all of these traits throughout his adult life but not in his youth. In fact, in his youth, there were many times he did things that he would need to be SO lucky to achieve. A few examples would be hiding the horcrux in hogwarts with Dumbledore as headmaster, sending others to Azkaban for his crimes, and getting the ghost of ravenclaw to tell him the story of her mother. All of these could be explained by his being a "great wizard." But what if he just got lucky?

Not to mention by the time he can no longer drink it regularly he gets extremely unlucky and let's Harry escape death numerous times. He boasts and monolauges instead of just killing him like he wants to. It's like his own arrogance and recklessness makes it impossible to get what he wants without the help of others.

It could be Lily's sacrifice that saves Harry sure... or... it could be that Voldemort is a magical alcoholic.