TL;DR version: Have your players missed something important no matter how much you wanted them to discover it? Have you as a player discovered that you missed something that was rather important and it wasn't due to bad luck with the d20 check?

I was playtesting Baldur's Gate III, and in one run-through, I had the characters attack and kill some groups of enemies without even attempting to engage in dialog. (Someone said they're bad=kill 'em first, and Speak with Dead after if available.) In that playthrough, the characters were oblivious of those enemies' connections and significance to the various over-arching plots (and rightly so).

That made me recall a DM who had to keep bringing up opportunities for the players to discover important lore for some of the various plots happening. One new player to the campaign immediately realized that there might be important information in something the other characters were ignoring and had ignored a few times prior before that player joined.

Because I'm the kind to look for everything, I feel that I've not missed important stuff given all the non-important stuff that the DMs have stated to my prodding (and possibly made up on the spot just for me—whoops!).

But what about you all?

We were in Icewind Dale and the DM made a big backstory for a goblin villain that we had to fight. Before we had the chance to learn anything from the villain, we persuaded the polar bears he was mistreating to rip him to pieces and devour his remains. So we ended up learning nothing from him. 

Moral of the Story: Don't mistreat polar bears.

I cannot think of a session where the players have Not missed something, or just as often decided they didn't want to pull any of the threads -- and especially not the one with the flashing lights and bright arrow pointing and saying here it is with rah rah music that only they can see and hear.

True story.

In the original Tomb of Annihilation, one of the first things PCs have to do is get into it.

Nope.

I have buried all manner of useful tidbits that are intentionally set up to be of value in the Campaign within the Lore books they have requested.

I have always just let it be. Because some of the best fun and greatest storytelling comes from what happens next...

I think it's important as a DM to - if you really need something to be discovered by players - they can "force" it to happen without railroading.

For the example of the OP, where players would kill, and Speak with Dead if needed; as a DM I would have had one of the enemies throw down their weapon, go to their knees and surrender - and hint to the players that killing an unarmed man might be considered evil, and that arresting him is the better method to go. And during this time, have the surrendering NPC blab out of fear, whatever lore the players needed.

Now, sometimes, players can act too foolishly, and miss repeated attempts, and then at that point - forget the lore, and just let it go and let the characters get punished (if that's what's going to happen) for not being more observant towards information gathering. If the players are murder hobos, there is often no point in trying to drop lore since they just want to kill. I've been blessed, since DMing, to have been free of the murder hobo mentality, but I believe that's because from the start, I inform the players that the campaign will be story driven; I am not looking to kill their characters, I want their characters to grow; but if they do something that is blatantly foolish, I won't hold back.

I've had a "shadow organization" hounding my party for a good while. In the past, during confrontation oftentimes one of the evil big bads 'The Overseer' would magically intervene by assuming control of one of the underling's bodies. This was fun both to drop plot devices but also to establish them as a ruthless and evil force. 

During one session a while back, one of my PC's parents were actively being kidnapped from town while the party had to fend with an attack force. Two of the members left combat to chase down the (flying) kidnappers. The Wizard cast dimension door and brought the Paladin. As they wrested the family from the evil's clutches, a non-flying evil NPC was taken over by the Overseer. He got two words out before the Paladin spartan kicked him off the flying platform, down ~300 feet. Splat. No lore drops this time. 

Every time the party plans their next move, this gets brought up. And we laugh about it every time. 

Was thinking about it, and remembered that the Mirror Rivals trope is really god for this.

That is, the party has a group of people who seem strangely familiar, but are also different that tease the hell out of them and mock them and the ret, but drop really useful inforation wheneve they meet.

They are rivals, so it is always like a kind of competition, and they can be used  over and over again (if the party kills one, they recruit a new member and remember that, if they kill them all, one somehow survives and builds a new team).

I gave my players a diary from the uncle of one of the characters who fell to demon worship. There are a few tidbits in there which may well come to light in the future, as the campaign progresses!