I know half the fun of the lair is finding new items, but once you've found them, keeping track of what's "new" and what you've found starts becoming crazy. I always am CONSTANTLY wondering "do I have all the lair items or is there another one that RNG hates me for?"
I propose a full list of the lair items, but with a twist. It'd be on the lair page and the item would only show up AFTER you've unlocked it in the lair at least once (per player of course, if that wasn't clear). For those you haven't unlocked it'd be a grayed out question mark instead. That way, we at least know if we've gotten them all, but maybe not which ones we're missing, so the mystery remains to some extent.
It'd also keep me coming back because I would know "yes, I am definitely still missing one and not wasting my time dumping items in here."
If the goal isn't mystery, then a full, always open list is totally up my alley too.