Hi, this is my first post on here!
I've always had a soft spot for Lissandra; she was my main mid/top from s4-s5. However, her passive has always been kind of irrelevant, and as Riot is currently struggling to find a new direction for it, I thought I'd give my thoughts on what her passive could be.
Ultimately, a passive should offer some new and interesting direction for gameplay that you can play around (Yasuo wind shield, Lucian double-auto, etc.). They should also, more importantly, resonate with the champion's design and theme. Lissandra generates Black Ice when she uses her moves, which is one of the hardest substances in Runeterra. Gnar was imprisoned for ages in there, and I feel the solidity of Black Ice should be present in her kit.
If we consider Lissandra's current passive, it basically allows you to use an extra spell every so often without its mana cost; this can come in handy during laning phase, but mana slowly becomes rather irrelevant, especially for midlane where you may be getting blue buffs and AP mana items. Moreover, what purpose does mana serve her thematic? Overall, this issue is tied to her lack of a defined identity, and ability to cover multiple roles. Is she a waveclear mage? Is she an AP burst assassin? Is she an AP off-tank? Or is she a battle mage?
This last option is probably the one that best suits her thematic and kit. She can damage multiple with her entire kit; other mages (Vel'Koz, Viktor) are much better at safe waveclear; other mages (Syndra) are better at the one-shot build; she doesn't currently have any intended resistances in her kit either, meaning she can't teally be an offtank (survivability through Zhonya's and her ult are not resistances).
This leaves us with battle mage, alongside Swain and arguably Mordekaiser. Lissandra thrives in the middle of the teamfight, where she can deal a lot of AOE damage, CC the entire team, and potentially survive due to self-cast ult or help isolate a target for the team with the enemy-cast ult. It therefore makes much more sense for her passive to be teamfight-oriented as well as the rest of her kit, aimed at increasing her willingness to make that flashy engage. Riot have tried to encourage this by adding a heal to her self-cast, but this felt rather like a slapped-on change.
My suggested passive would therefore be one that matches both the character's thematic and her kit's execution:
Whenever Lissandra applies crowd control to an enemy champion, she gains +X (+ X per level) armour for 3 seconds per each champion affected.
This passive matches her theme and makes her more survivable when engaging. Lissandra should be rewarded for landing a 5-man Ring of Frost followed by her ult, not for sitting back and spamming spells.
Thanks for reading my rambling first post! Again, this is simply my thought process of how her passive could potentially work. Please let me know if you have any thoughts or comments :)