She is definitely VERY unhealthy as a champion...her kit is basically:
Passive: Additional Damage Steroid.
Q: 80% slow at ALL LEVELS. SEVEN SECOND COOL DOWN.
W: One of the strongest movement buffs in the game / A suppress that allows AND ANOTHER SLOW. TO 60 MOVEMENT. 18-12 second cool down.
E: A shield/target damage to an enemy. On enemy? Grants Vision, and when she Q's, pix point blanks you. 10 Second Cool down.
R: Massive heal, Knockup, AND ANOTHER SLOW. 110-80 second cool down.
So basically - you out ranger her, and she can do nothing, and is going to have a negative experience; or you never get into combat, and she spends the entire game running and poking, and YOU have the negative experience.
In short, lulu has SOME FORM of CC (counting vision) on EVERY ability, and no reason to ever be closer than 550 range. Her basic attacks are the shortest range she has. Her W and E are 625, and her Q is 925.
HOLY CRAP. Now that i'm through that side of the pose, here is what needs to be done.
Passive: Fine.
Q:Lower the slow to something reasonable - say 20/30/40/50/60(+5% AP)?
W: Just - Just no. Get rid of the suppress. If NOTHING ELSE, this should be the flip side of her ulti (the enemy cast vs ally cast thing she has going on) - even if it IS removed...the cool down or the movement buff need to be SHARPLY brought to heel.
E: Not too out of control....but give it a scaling cool down. It is very hard to escape a gank through the jungle if the enemy jungler know where you are. So make her DECIDE when to use it, rather than allow her to spam it from level 1.
R: I fine.
TL;DR? Better nerf Irelia.