That innate is crazy powerful.
Attack speed reductions stack multiplicatively (with the sole exception of Randuin's Omen's passive), and take percentages off the final attack speed value after all bonus attack speed has been factored in.
40% AS is the equivalent of a level 3 Malphite Slam, (which also lasts for 3 seconds) so this character, if she spaced out her spells could completely negate the enemy ADC. Think of it in terms of counterplay as well.
For a malphite to achieve the same effect, we would need to be up close to an ADC, he can use his ulti to close the gap, but what if the ADC is ezreal and simply shifts away? Now malphite q's him and chases after and applies the slow. However now he is horribly out of position, and has no methods of escape. For Lissandra, she simply has to q the target. Attack Speed slows, are incredibly annoying to play against. Because not only do you attack slower, the animation itself is slower, so it takes more time for an attack to occur. This is why Malphite, must work to achieve his hefty AS slow, because it has to require him being potentially compromised, thus balancing out the fact that AS slows are annoying. There are options for avoiding it. There are times when Malphite can just ulti the carry and then get his slam off, and that is due to bad positioning of the enemy ADC. Lissandra has two spells that bounce off the main target, and can punish an ADC for staying away from her. (In the backline, where they are supposed to be.)
Other AS slows, like Gragas Barrel which is a skillshot, and thus not guaranteed to land, whereas Lissandras is on her passive, and is tied to all of her spells, most of which hit additional targets, and are targeted (as opposed to skill shots which must be aimed.)
This passive alone, without the splashing effect is incredibly powerful. Considering the passive proc's if they are affected by any spell (not necessarily the main target.) I recommend a drastic change to this passive (perhaps only the primary target of a spell takes a slow ( and one that is down-toned at that))
I like the concept, and the spells seem like they have plenty of ways in which you could master this champion, you proposed that this should be a tutorial champion. The skillset is very complex (compared to ryze) and I do not think it is appropriate as a learning champion because of the skillcap this skillset would produce.
E seems like massive power creep on Morgana's shield.
The ulti seems like it can be used negatively, for example Lissandra ulti's a target who Caitlyn is ulting and as a result accidentally saves the enemy. The spell itself is an interesting idea, however she may ulti a target in a teamfight, only to have the enemy saved instantaneously by AoE's. It provides too many options where it is actually the wrong choice to cast the spell. Due to the complexity of the spell, it actually creates a confusion of purpose and counter play. For instance, an enemy team sees their carry get ulti'd. They ideally break the shield and save their friend. But alternatively they might simply target Lissandra, forcing her to abandon her quarry to save her own life, thus making the shield itself kind of redundant. If the shield's strength is too high, it means that attacking the shield is a waste of time, and thus it is simply not a realistic option. This provides false choice for the enemy (similar to Strygwr's ulti). However this cannot simply be combated by lower numbers, else the shield would be cleaned up by aoe spells and be negligible and thus a wasted spell for the caster. It is a fantastic concept, however in reality it doesn't really play out as you would expect.
I apologize if this comes across as rude, I merely play the devils advocate.