Lux vs. Zed: What a friggin' obnoxious lane matchup...
Harass him? Zed's tend to rush Bilgewater Cutlass, and his 7.1 base HP regen is enough to shrug off the amount of harass Lux can safely send his way. Once he has that lifesteal, harassing him is worthless, and going in to trigger your passive on him will get you killed. Early on, he can also trade favorably against you with his W+Q combo, since you'll run OOM quickly if you use E+W and he'll never run dry.
Passively farm? Zed will zone you, forcing you to farm with Lux's underpowered E, which costs too much and doesn't do enough damage to oneshot the lane minions. Going in to autoattack farm will just prompt Zed to dive you.
Rush armor? Lux will suffer frequent mana burnouts as a result, so all Zed needs to do is force a long-term fight and he wins. Besides, Lux is too squishy for armor to make any real difference on her. To her, it's mostly a trap stat.
Snare him? Trying to throw your Q at him will generally result in him dodging it, and then going all-in on you because it's on cooldown. Throwing it onto him after he dives you won't help either; he'll still rip you apart. You're dead!
Did I miss anything? Downvote away, but it doesn't change the fact that Zed is a total bastard to fight mid-lane.