I get what she is supposed to be, but just because she is SUPPOSED to be that doesn't mean she feels that way...my fiance has been playing this game for around 4 years and absolutely loves Lissandra and he still feels her kit would feel much better if she played more like an all in kill one target and screw over the rest kind of mage.
She has the tools to be a control mage but she still feels like a mage that should be going in to "nuke" a squishy champion be it their adc or mid lane. Besides tank counters nuke AP casters, wouldn't her being a more burst mage make her not a "Bullshit top laner" anymorr? Wouldn't that be a healthy thing? A good thing?
And furthermore, as a control mage, her ranges really are too low (unless she is top) to really control much of anything, and this is why she feels more like a bursty anti assassin kind of mage in lane. In lane she doesn't control jack shit, I mean she has poke? I guess? Maybe, no, not really in mid lane unless she is against an assassin with bad laning. Sure she has control for fights but unless her team has CC to help her go in and properly get everyone in her root/ult or if the enemy team is dumb enough to actually not scram when they see her E coming she won't be accomplishing anything at all.
A control mage should be a mage that can control a zone of the lane/ map to their advantage and make it harder for the enemies to progress or come near them. Examples of this kind of mage are:
these are the best at fulfilling that kind of role. Lissandra is more of a disruptor and works on splitting the fight up. She can be called a "team fight control" mage but a lot of champions can be considered that and so it isn't really something she fits in. To me, and it is just my opinion, she feels, through her kit, like an anti assassin burst mage or all in burst. That's how her kit feels and would feel more fluid if it was played as such.
Don't get me wrong I love Lissandra but she does need help.