It is rather ironic that Lysander says this quote at the beginning of the play, reflecting only on the troubles that he and Hermia have already experienced. The rest of the play clearly shows how this statement is much more far-reaching and does not exclusively apply to the four Athenian lovers--it could equally apply to Titania and Oberon or Thesues and Hippolyta, for example.
However, Lysander and Hermia have already experienced the truth of his words through the way in which Egeus, Hermia's father, is bitterly opposed to their love, even to the point of losing his daughter if she refuses to marry Demetrius. Demetrius and Helena too have their love thwarted. Demetrius loves Hermia at the beginning of the play, but Hermia's love for Lysander prevents him from gaining Hermia. Helena loves Demetrius, but the way in which Demetrius is so fixated on Hermia means that Demetrius is all but blind to her existence.
What happens during the rest of the play also supports Lysander's statement, as the change in the affections between the four Athenian lovers shows. One falls out of love and then in love with somebody else, and the situation gets incredibly confused as Hermia moves from being the desired object of both men to suddenly finding herself spurned by both as they both desire Helena. "True love" is soemthing that rarely seems to be accompanied by smooth transitions in this play.