Demonstrate it to the PCs
The key problem with these complicated mechanics is that it's very difficult to telegraph them to your players. Video games can get away with complicated mechanics because they can highlight weak points, and the full range of actions a player can accomplish are limited by the game. In an RPG, where players can attempt anything they can think of, the range of possibilities is enormous and insurmountable, especially when there's a lich trying to kill them.
If you don't want to tell the PCs outright, with an NPC or some other clue, you could demonstrate the weakness. Have the Lich be noticeably afraid of bones, and emphasize his caution around his minion's bones. In another case, you could show a minor accident that causes an outsize amount of pain to the boss, like dripping water on a fire-based creature or something.
It shouldn't be hard.
When you're building a puzzle like this, it's easy to be too subtle about the clues. Remember that the PCs are receiving a constant stream of information from you, some of which might not be relevant. Unless you want them to waste time obsessively scrutinizing everything you say, you should leave multiple hints that seem obvious to you. After all, the negative implications of it being too easy are pretty small compared to the TPK that happens when it's too hard. For example, bosses in the Legend of Zelda series almost always have a big, colorful weak point that's obvious in their introduction cutscene.
The stakes and the difficulty are inversely correlated
In the Lich scenario, the PCs are actively being killed, and don't have much time to spare. If they waste a few rounds doing something useless, the consequences are dire for them. Therefore, the puzzle should be something they can figure out in one or two tries, because they might not have more than that.
On the other hand, if the Lich is already dead and the PCs have his phylactery, the stakes are much lower. Nobody's trying to kill them, and the PCs have a few days to figure out how to destroy it. In this case, you can make the puzzle a lot more complex and subtle, since your players can afford to spend time trying different things.
In the middle lies a weak boss, who can't deal too much damage. If you tone down the power of the boss significantly, so that neither side can easily defeat the other, you open more space for the characters to work out a puzzle boss while still keeping some pressure on the PCs. Of course, you'd have to make the puzzle interesting, or else it just becomes a big slog.
I have now DM'd the final boss fight myself. So, as no one with direct experience has thus far responded to the question (though many of their suggestions were good), I've written up my own experiences, detailing what went well and what went badly. Hopefully this will be useful to the people who have favorited this question, some of whom may be currently DM'ing LMOP themselves.
What approaches have you used successfully in your own game to make the final encounter with The Black Spider 'memorable and exciting'?
- We'd played the entire campaign up to this point in the theatre of the mind. Suddenly revealing a full map and playing pieces for this fight definitely added excitement and grit, it also really helped to keep track of the AOE spells (faerie fire, web, darkness etc.) rather than me feeling like I was fudging who was hit and who wasn't.
- I decided to add hp to the Black Spider and turn him into a 'paragon monster'. As the final boss, I didn't want him going down in just two good hits, so I decided to give him two separate hit point pools of 37 hp each - when he went down the first time he 'regenerated' into a more dangerous final form (two turns per round) which really appealed to my players, familiar with boss fights in pc games, and made the Black Spider feel appreciably different to any boss they'd faced before.
What approaches have you used successfully in your own game to make the final encounter with The Black Spider feel balanced against a larger sized party?
- As mentioned above, I added extra hp to try and slightly balance out the action economy.
- I added two extra giant spider minions (bringing the total to six). Having as many spider minions as PCs definitely added to the drama and the spectacle but if the rolls had been more on my side this could have been a bit too much.
- We used milestone levelling, so I decided to keep the party at level 4 for this fight. Fifth level would have removed a lot of the danger, half of the party would have gained Extra Attack, not to mention the extra HP, spells and proficiency bonus increase.
- I treated the Black Spider as a fifth level caster (as opposed to fourth level), so that he rolled a second damage die for his cantrips.
What would I do differently if I did it again?
- The Black Spider is fairly toothless once all of his minions have been killed as most of his spells are crowd control, rather than damage dealing (only cantrips and magic missile, melee a last resort). If I was redoing this fight I think I'd give him the option of one scroll of fireball, to be used if the fight was going too quickly south.
- Make better use of webbing as difficult terrain in order to crowd control the PCs.
Best Answer
Give them minions like Stormtroopers or Battle Droids.
There's a number of scenes from Star Wars media where this sort of thing happens - just off of the top of my head, one of the first scenes where Darth Vader shows up in Star Wars Rebels involves him attacking the protagonists and engaging the group's Jedi in a lightsaber duel while his stormtroopers get into a gun battle with the blaster-wielding rebels.
Moreover, because you're playing this game using DnD 5e rather than one of the numerous Star Wars games, you've got the advantage of 5e's Bounded Accuracy design, which means that low-level foes are still capable of credibly threatening high-level players, since leveling affects damage and HP much more than it does accuracy and AC.