I am really not terribly familiar with FR, so I actually have no clue how common knowledge Valindra being a lich is. Like is she a famous person and famous for being a lich? Or is her being a lich some sort of secret that only very few people know? In any case, the player probably should have just said to the GM: 'Does that name ring any bells, can I roll history or something?'
Well, in the case of the DM not knowing such a detail, which I think was largely the case in the OP....they can simply decide how famous she may be. Same as if it was any other NPC.
And while I have no problem at all if the player did have the presence of mind to not blurt that out, but instead to ask if they might know of the NPC in some way...I just don't see it as necessary. There's nothing about the adventure that relies on the PCs knowing or not knowing who Valindra may actually be.
What if the situation in the OP was a bit different, and a DM just says "Valindra has an infamous reputation along the sword coast as being a power hungry schemer, and many even claim she's undead." Would this be acceptable?
Anything is 'possible' in fiction so that is a too vague. But whether the character has heard of this lich is a fact about the world, thus ultimately for the GM to decide. And players are supposed to play their characters as consistent people in the setting and just deciding out of the blue to think that a random person is a lich with no clue or knowledge is not that. (Unless this is something related to the character's established personality. They of course can be paranoid and think every person they meet is some sort of monster in disguise, but this was not the case here.)
This implies to me that what you're most concerned with is maintaining the DM's authority when it comes to establishing fictional elements. It's not so much about the verisimilitude of the PC knowing something like this.....we could craft any number of fictional reasons that they may have learned of something like this at some point.
So, if that's the case.....then I think the questions become "why does the DM need to have such authority?" and "can such authority be shared a bit with the players?"
Looking at the Forgotten Realms fandom wiki, there are a number of ways a PC could potentially know who she is - but the knowledge is pretty specialized considering her membership in secretive organizations and adventures in weird places, and some of which were a century ago. But the chances of her being known to players is relatively high, having appeared in 3 computer games and something like 5 novels as well as a comic book - though apparently not as a lich in all of those outings.
But ultimately, it's a bit like drawing a line between 3rd person omniscience and 1st person perspective. The authors offer up a certain amount of omniscience in their books. But not every character is privy to it. And that's why I think the player should have pulled the DM aside when they realized they recognized the NPC to hash out what they might or might not actually know.
Sure, it might be specialized knowledge in that the average person doesn't know she's affiliated with evil organizations and that she's a lich. But certainly some folks know those things, and certainly those folks might talk to other folks.....and so on.
This specific example doesn't seem incredibly likely to come up all that often, right? Not unless the DM decides to actively drop all kinds of existing FR NPCs into their campaign....and if that's the case, then I would think they're actively promoting sharing player and character knowledge of these characters, or else they're setting up a potentially frustrating play experience. As mentioned earlier by
@Ovinomancer I think.....metagaming is really a problem that happens at the DM level.
The problem here is that the character may be thinking and acting on something that is unknowable to the character and is doing so because the player is interjecting something they know into the situation because they encountered the information elsewhere.
I know this bit was not directed at me....but how can we say what may or may not be unknowable to a PC? I mean, there are going to be some very easy examples we can think of in both categories......but aside from those obvious things, there are going to be a whole slew of things that we wouldn't know for certain if the PC would, could, or should know.
How do we determine that? Who gets to decide? Why?