Reverting Open Parties and Claims to 0.12 fixes the issue.

Full log: https://mclo.gs/oXhUOtB

Error part:
[11:44:45] [Server thread/ERROR]: Mixin apply for mod lithium failed lithium.mixins.json:ai.nearby_entity_tracking.ServerEntityManagerListenerMixin from mod lithium -> net.minecraft.class_5579$class_5580: org.spongepowered.asm.mixin.injection.throwables.InvalidInjectionException Implicit variable modifier injection failed in net/minecraft/class_5579$class_5580::updateEntityTrackerEngine [INJECT Applicator Phase -> lithium.mixins.json:ai.nearby_entity_tracking.ServerEntityManagerListenerMixin from mod lithium -> Apply Injections -> -> Inject -> lithium.mixins.json:ai.nearby_entity_tracking.ServerEntityManagerListenerMixin from mod lithium->@ModifyVariable::updateEntityTrackerEngine(J)J]

Thanks for reporting!
I am able to reproduce it but it's super strange. I see no reason for the mods' mixin injections to conflict there. I think this might be an issue on Mixin's or Quilt's end. It does not happen on regular Fabric.
What's weird, I don't think this injection that Lithium is making is even allowed. It's supposed to crash by default as I understand @ModifyVariable, but I might be wrong. In that case, my mod somehow makes Mixin work like it's supposed to. But if I'm right, it should be fixed on Lithium's end.

Thanks for the response!
Should I forward it to Quilt/Lithium?

You should probably start with Lithium because I don't think @ModifyVariable works with RETURN codes.

Thanks, opened CaffeineMC/lithium#394
Closing this one.