How long has Lysander known Hermia in A Midsummer Night's Dream?
Lysander has not known Hermia very long, but they are very much in love.
Although it does not directly say, we can infer that Lysander has not known Hermia long because Egeus would not have waited to come to Theseus. He likely came with his daughter as soon as he found out that his daughter’s affections were not with Demetrius.
This man hath bewitch'd the bosom of my child.
Thou, thou, Lysander, thou hast given her rhymes,
And interchanged love-tokens with my child;(30)
Thou hast by moonlight at her window sung…. (Act 1, Scene 1)
Egeus describes what seems to be an aggressive courting of Hermia on Lysander’s part. He wrote her poems, gave her gifts, and serenaded her. Egeus says that he “Turn'd her obedience ….To stubborn harshness”(1:1), so we can assume that she has been a good, obedient daughter until now.
Relationships are rather fickle in A Midsummer Night’s Dream, even before the potions. Although Demetrius has been in love with Helena, he apparently decides that Hermia is a better catch. Egeus wants him to marry her, and he complies.