With Lucian, it's fairly simple. The contract does not extend towards the lesser, non-champion Shadow Isles denizens. So he still can slaughter undead on mass and fulfill the purifier's oath (Slaughter undead on mass). What you must realize about the Shadow Isles champions is that they are, for the lack of a better word, contained. Not like Nocturne or Brand, not a full prison, but they're kept in check.
Hecarim's essencially a vanguard, after arriving to continental Valoran and making his show of force, he can't do shit. He, like Mordekaiser, are field commanders, and field commanders are nothing without an army, something they lack (or lacked. The new Black Mist says otherwise).
Karthus' intentions are very unclear.
Evelynn... well, what the fuck is even evelynn?
And Thresh is essencially in an amusement ride already, in the fields. He doesn't need to go out and kill more people, he already has all the people he can torture here (The best and brightest of Valoran).
Joining the League, Lucian can keep tabs on all these mofos, and strike first if they try anything.
Lissandra, on the other hand, is a politician. I think they fucked up real time by telling us the background face-first, instead of keeping the revelations and machinations to a Judgement (sigh... remember those?), because the Backgrounds were supposed to be the public info Valoran's population got to know about champions, while judgements were private, and sometimes the knowledge of what happened in there was limited to two people: the Champion and the Summoner (Example: Swain's Judgmenet, also known as "How to write manipulative bastards wonderfully").
Without the balls-on-face background, you could justify her entrance to the League as a way to gain favor and political power. All the nations worth their grain of salt are in the League. Most political leaders are in the League (And I'm pretty sure champions cannot truly die outside the League - Half their soul is stored within a Central Nexus, and when they die their bodies are simply healed and the soul re-implanted, and re-divided). What would say of a Leader who refused to seek representation in the magical equivalent of the UN?
OR, OR, the more likely, forth-wall-breaking explanation is this: Riot didn't make Lucian's and Lissandra's lore with the League in mind. Ever since the Katarina lore rework the League has been a backdrop barely mentioned if at all. The lore team themselves said they were planning a retcon or something similar for a long time. The most likely explanation is that new champions like Lucian, Jinx, Lissandra, Gnar, Syndra etc, were already wrotten lores in a universe where the Institute of War does not exist. You can notice all champions before NewLore! Kat have at least coherent, at most ingenious, reasons to join the League. After that though? Varus. Nautilus. And I don't even remember if they came before or after. Besides those two, most champions felt almost detached from the lore, because they were. From the old lore. They fit PERFECTLY in this new lore, where we have this expansive universe with no such thing as a narrative or focus uniting all its loose threads.
Say what you will about the Institute, it gave the world a raíson dêtre. It gave it unity, focus and a reason for these people to interact. It was purely unique, and well handled it had the potential to shine a new light in the fantasy genre, by taking what is usually considered the most boring part of it (Politics) and creating interest, builing an entire universe about it, and giving the world a feeling that it made sense and might exist far bigger than most other fiction works.
Without it, we're basically reading "Baby's First RPG" without one (or many) focused narratives to create interest besides the initial wow-factor.
The new short stories are good. Very good in fact. Sion and Amumu were awesome, IMO. But that's what they are. Short stories. The only recent time Riot tried focused narrative they failed spectaculary (In my opinion, the Shurima story was one of the most embarrassing excuses for a convincing story I have ever read. It felt like a stew of clichés, and to add insult to injury it took a character which was compeling, tragic, and just damned well written (xerath) and turned him into a Jaffar wannabe, without even having the stones to go all the way through, leaving us with a very bland, very boring character which we have already read so may times already.
Xerath is the perfect example of the plain disrespect Riot has for its previous works. A character defined by its self-sacrifice, driven by a desire to discover, to know, by curiosity, one of the most fascinating emotions the human being is capable of, is now driven by a simple desire for vengeance. Before, Xerath could care less about the men which imprisoned him (Paraquoting: "I care not for something as petty as vengeance. Dust has erased the legacy of the old mages of Shurima, and only I remain). He was superior, he was better, HE WAS ASCENDED. Before that word lost all its meaning, he was ASCENDED. Now, what is he now? His entire life is dedicated to one man (To bring him down, true, but compare it to old Xerath, whose life was dedicated to a concept, noble one at that: knowledge), he didn't spend years obtaining his power by his own means, power such his body could not contain it. The Ascension he suffered was not the next step through on a path of a gifted, yet misunderstood man, it was the undeserved theft of a blind coward, who did not even try to warn his, by his own words, brother, after he realized he had been wrong. Both thirst for power. But old Xerath earned it. He payed for it in blood and flesh. The new Xerath took it. He payed for it with the blood and flesh of his peers, of tens of thousands of innocents, suffering nothing for it and showing no regret whatsoever after the deed was done, only a slight bit before, a bit so slight it might as well not be there, which changed absolutely nothing for the story.
So, is the new lore good? Some of it, yes. Was the removal of the Institute of War and years upon years of lore and emotional investment justified? Perhaps. I think not, but perhaps. WIll I ever stop being bitter, and care about anything else they write? No. Fool me once, shame on you, fool me twice, shame on me. I refuse to get invested on a universe its damned creators can't care enough to try to iron its edges, instead choosing to completely destroy it and rebuild anew. What's stopping them from doing it again? What's stopping future years of caring about the characters and world going down the drain, because the next batch of writers they hire don't care much for this new story?
Writers have the right to chance their world as they plse. The audience has the right to tell them to royally fuck off after they do so. And such is my right. I'm willing to discuss the validity of my points, but my emotions are simple: Almost nothing they write will be able to hold me in the same way the old lore did, or hold me at all. I stopped caring, and I see no reason to do so.
. Why would he ever join the league? He's on a quest to exterminate all undead. He truly hate them all, no matter if they're actually evil or not. Joining the League would put him under a contract to never atempt to harm another champion outside of the Fields of Justice. This includes several of the Shadow Isles leaders, as well as his arch nemesis who has stolen his wifes soul and put it in a lantern. On top of that, he has to interact with and fight alongside them on a regular basis. From what I know of him as a character, this would be straight out torture.
is another great example. She has this great, secret plan and nobody knows her true identity. Let's join an organisation where you litteraly have to share your mind with god-knows how many people, who could the super easily find out all your plans and ruin what you've spent hundreds of years planning! I know all summoners are under a strict code of silence, but come on. A champion is litterally planning on freezing the entire world. Isn't this exactly the kind of thing you're trying to prevent?
(he probably wouldn't really understand the concept of the league),
(because monster duh)&
(he seems to be really mad,maybe too mad to think about something like this).
for instance. So it does broaden their ability to make characters and tell stories.