Lysander is one of four lovers in the play. He loves and is beloved of Hermia. Demetrius is his rival for, not her affection, for Lysander has all of that, but for her hand. The two men are often considered to be somewhat interchangeable, as do the two women Hermia and Helena, and, in fact, through the offices of the Fairies, they actually do find themselves switching partners, or trying to, several times in the course of the play without missing a beat. Lysander is unimportant as a single character. He is a vital part of an extremely dynamic quartet, whose role it is to express the kind of young, brainless, quixotic, passionate, inconstant, rumble-tumble love of the young. These four form one of the essential love themes in a play that is like a concerto to Love.
Lysander is the youth in love with Hermia. Their relationship is strained because Lysander cannot marry and love her openly due to her father's wishes. Hermia's father wishes for her to marry Demetrius instead. Eventually, Lysander and Hermia will elope. The two will get involved in a tangle with Helena and Demetrius when Puck's love potion tricks go awry.
Lysander is a character in "A Midsummer Night's Dream". He is specifically Hermia's boyfriend, and they run away to elope. Puck accidentally squirts love juice in his eyes and when Lysander wakes up he then falls in love with Helena, following her around trying to win her over. Lysander is quite often compared to Romeo from William Shakespeare's "Romeo and Juliet". He is a hopeless romantic despite the major obstacles he faces in pursuit of love. Hope that helps some!