1. Do you think I did anything wrong and how am I supposed to play this? I can't like forget that she is an evil lich.
Of course you did wrong. Of course! You can just assume anything, but the whole reason there's a system of rules is to keep you from jumping to conclusions and running with your assumptions. "I have 18 Int so I assume I've heard her name before and know her best-kept secret" is no different than "I have 18 Str so I assume I kill the entire tribe of troglodytes and loot all their treasure." No need to play the game! Just ask everyone what they expect will happen and pretend that's fun, somehow.
You didn't do anything in the game world, as your character, to find out she's a lich. As a player you have to grab that knowledge nugget, wrap it in greasy foil, and slide it back behind the frozen peas in the freezer of your mind. You still have it, but you'll never see it again. Because you
don't actually know she's a lich. Your DM might have changed the lore for this game, or this could be before she became a lich, or she's lying about her name. So that knowledge is something you can think of as a possibility, but it's not a given. And as you play, you have to remember that your character
does not have your knowledge. Your character doesn't think of her being a lich as even a possibility.
Part of the fun of D&D is discovering new things. Even when it's something you expected, assumed, or knew because you read some other book, it's fun to go through the process of finding out what the DM has in store for your game. That discovery might not come until the lich reveals her true nature and kills your favorite NPC, but even that is lots of fun. That's the story you're telling through the process of playing the game, and it's an important element. You completely sidestepped it and shot a big hole in a lot of potential fun for your entire gaming group by blurting out that she's a lich.
Step-be-step, here's how you should have played it:
1. I don't really
know she's a lich. My character doesn't even think it's possible. I'll keep this to myself and find out what the DM has in store for this character.
2. My character meets a friendly elf and learns her name. What would I do if this were anyone else?
3. The DM is going to drop hints about this character if she has any backstory at all. I should pay attention to those. Maybe I'll make some good rolls to find out she's a lich, or that she's something else entirely.
4. I accept that if she's a lich we'll get to have a cool enemy, and she'll be more connected to us if she was once a friend. This will make the game better, and I shouldn't ruin it.
2. What do you think of our strategy to eliminate her?
I think it doesn't matter. The DM already let you use metaknowledge to sidestep most of the challenge she presented. Just grab the piece of paper with her stats and run off with it. There, she's defeated. Might as well.