Lebeau, in Miller's play Incident at Vichy, is a character who is ruled by fear. He is twenty-five years old, a painter by trade, and does not care much about his personal appearance.
In 1939, as Hitler is approaching France, Lebeau is ready to leave for America, but, sadly, his mother cannot bear to part with their furniture and they miss the opportunity to escape.
Lebeau tries to cling to the hope that the Nazis do not have any other agenda other than to ferret out spies or to seize workers for their coal mines. Of course, this is delusional.
As the characters all await their summons to the Detention Room to be interrogated to determine if they are Jewish, they take turns speculating about what will happen, and perhaps more importantly, why it is happening.
Lebeau offers what is perhaps the most reasonable explanation of the atrocity: there is no explanation. There is no point in suffering, no grand lesson to be learned, internalized, or enacted. He talks about the lack of meaning in his own paintings and how people try to find a pattern or a message within the abstract. There isn't one, and there isn't one here, he argues.
Lebeau's significance, then, is that he brings the voice of the Existentialist to the play. In the early 19th century, the philosopher Soren Kierkegaard argued that only the individual can determine meaning for his life alone, and that there is no avoiding obstacles such as despair and absurdity. Lebeau, though fearful, subscribes to this philosophy. Leduc, who also awaits his fate, comes to believe in much the same way. He says to the others, "You cannot wager your life on a purely rational analysis of this situation. Listen to your feelings: you must certainly feel the danger here.”
The only way for an Existentialist to overcome obstacles is to face them. This is what Lebeau and Leduc are trying to do.