Lissandra has always been popular (but recently a few Pros started playing her in competitive play) which probably propelled her to the "meta" and you see her more often.
CC as Janna
Lissandra is arguably a CC queen since 3 of her attacks have some sort of CC. For this, I'd say she's different from Janna since her CC's are more about combo instead of supporting.
the damage of Annie
I would say Annie provides much more damage output. Annie is a burst mage AP in which she has a series of combo to burst her opponent down coupled with Tibbers and her shield. Lissandra does not have the same AP ratio in her attacks as Annie which makes Lissandra's nuking capability weaker unless she gets a good amount of AP items to compensate.
the mobility of Zed.
Lissandra has the slowest projectile for mobility-type-moves. Lee Sin probably has the fastest. And Le Blanc and Zed has instantaneous speed in mobility (in their respective skills) If you compare Lissandra to those other types of champs, she's not very mobile at all BUT has enough mobility kit for initiation.
Verdict: She's not OP, but skilled players are using her and now she's in the meta.
:D