Lane bullies that bully better than Lulu:

Enchanters that outclass Lulu:

See, here's the thing: Lulu is a generalist. She can do a bit of everything, but isn't particularly great at any one thing. She also has no sustain, and her shield has a lengthy CD. So, pick someone long range, with a lot of bullshit damage that she can't sustain though, (Sona, Nami, Zyra, Brand, etc.) and wow, you won. However, pick someone who relies on going in and one shotting the carry, and you won't do a whole lot if the Lulu is any good.
As for her "unavoidable damage"... if she gets in range to cast E on you, and actually chooses to use it on you instead of her carry or herself (meaning you're not pressuring at all), then you deserve to get hit by that. Her Q is easily avoidable since it moves so slowly -- and if you stand behind minions it does FAR less damage too.
If you wanna talk broken supports, let's look at Alistar, Nami, Sona and Zyra -- with a bit of Janna thrown in depending on how you think.