The name Lysander is a Latinized form of the Ancient Greek name Lysandos which means "a release of a man". Lysis meanin "a release" and andros "of a man".
Shakespeare could have possibly chosen the name Lysander to be one of his charatcers. This is because Lysander seems to be a very passionate and poetic man throughout the play. He doesn't hold back his emotions, and is always releasing his thoughts. Thus, the meaning of Lysander, "a release of a man," fits the character Lysander well.