I may be wrong but Phyrexian mana counts as cmc so Dismember wouldnt work. Also I love Lili and I think it would be great here if you get the budget.

I_Want_To_PlayAllTheDecks "Permanents"

oh oops :P

Also- Lurrus is kinda a no-go with lurrus cuz it has lifelink.

Well, lifelink is actually pretty good in this deck, because the lifegain is optional in a sense that I can choose not to attack or block with it, but can do so when I'm in trouble (Game 1 vs Burn for example). Can always lose more life for the Death's Shadow. Lurrus' resurrect ability is pretty bananas as is, but the lifegain actually pushes it over the top for me, plus the fact that it's basically always in my hand being a companion.

Add at least 1x Necrogen Spellbomb. It allows you to have a permanent instant speed discard, winning by itelf most matchups.

SinsOfTheMoon doesn't really fit in this deck. It only supports synergies between creatures and non-permanent spells

Humm, maybe you didn't realize this very easy lock it creates with Lurrus' ability to cast it back from graveyard every turn, making it a permanent instant discard for 2mana (1 colorless during your main phase, then 1 black mana after your opponent's draw step to make him discard that card he just draw). I believe its the best possible interaction Lurrus can have with a card.

Or... maybe you missread Lurrus' ability to cast non-permanent cards?

I see that interaction, but still. I'm not even saying they don't interact well, I'm just saying this interaction wants a different build-around. Un-targeted discard like the spellbomb will always take their worst card, unless they only have 1 card in hand, but in that case I better not be behind on the board. The spellbomb has no interaction with my other spells. I'd much rather resurrect my creatures, especially snapcaster mage, for a two-for-one interaction. I'd also like me playing the companion to be optional in any game, but the spellbombs would push me to play it every game. Again, I'm not saying your suggestion is intrinsically bad, but requires a different buildaround and I'm not willing to make the changes. That would be a different deck.