Anivia's new skin makes me think it's legendary tier.
According to her new Lore, she's pretty much the living embodiment of Freljord, and it mentions the Darkness of Freljord could (and would) dominate her if it isn't stopped, this new skin makes Anivia a bit on the dark side of things, making me think that's an Alternate Storyline, kinda like Aether Wings Kayle.
That plus there's too many new particles (and a new voiceover too) for it to simply be 1350RP. :V
As for Lissandra... She's weird.
I mean, her pushing potential is off the damn charts, between her E, her W and her Q. And even with just her Q, her ratios are high enough (and its cooldown low enough) that she can make a pretty good effort pushing a lane.
The EEWR combo is kind of hard to do because you just need to be so quick about it, BUT it can also deal some pretty ridiculous damage, lol.
One of her recommended items is zhonya's and I can see why: Anything besides her Q has ridiculous cooldown, so QEEWR buys her 1.5 seconds, zhonya's buys another 2.5, enough for another Q and about half of her W.
She's gonna need cdr, almost as badly as lux, it seems, but it's going to pay off.
Overall, she seems pretty interesting and a damn good AP Carry, though she isn't an initiator by herself, she's more like an extention to another champion's initiation considering her E is so slow moving :/
She's kinda like Katarina as in she needs to jump in to do her full damage, but unlike katarina, she doesn't NEED to wait for enemy cc to do so, especially considering W has no real animation and does not stop her movement.
As for how well she'd do as a support, this is theorycrafting, but she's 100% viable, not the best option, but quite CERTAINLY viable.