Does hermia and lysander get married?

She does, eventually. However, at the beginning of the play, her father invokes a law which says that she must marry the man he chooses for her, or become a nun, or be put to death. Lysander is not the man her father chooses, so none of the legal options involve Hermia marrying Lysander. However, she and Lysander go for a less legal option: skipping town and eloping somewhere else.