For me, these two posts taken together are a bit hard to follow.
Just focusing on the ongoing or unfolding fiction, what that consists of and what is authentic to it seems to be something within the scope of the GM to decide. Eg the GM could decide that there is some reason the lich doesn't conquer the kingdom (for whatever reason), or the GM could even just leave the lich issue in the background (as happens quite often in serial fiction).
So the GM treating it as important to nevertheless follow through on this bit of fiction in this particular way seems like it the GM deciding to render something salient in play that is quite separate from the characters.
Something is introduced into play, lets say rumours of there being giant attacks. Rumours become facts, and attacks seem to increase in frequency. There is a sharp inflation, perhaps a shortage of some material, trickle of refugees - all due to the actions of these off-screen giants. Characters can either get involved and investigate or carry on about their business or take on another quest.
Essentially, what has happened, the DM has introduced the beginnings of the Storm King's Thunder AP.
If the characters do not participate, I'm not suddenly going to hit pause on the background.
Or if the characters disappear for two years and come back and then ask hey what happened to those giant attacks. The DM isn't going to say, oh nothing because you weren't there. That would knock my players right out of storyline and I prefer to maintain some sense of immersion.
The difference with
@hawkeyefan's game and mine would be that for his table they've drawn up characters specifically for that module and that is it. No downtime, no character development, no nothing is going to happen, because there is no opportunity. The game is strictly about the Temple and beating it. That quest cannot be abandoned or paused. The characters will be dropped after the module.
In my game, there is character development (cleric recently suffered a crisis of faith - the cleric has not been praying for his spells and put the party at some risk), character story arcs and goals will be explored (just closed off a character's backstory, goal was accomplished). There is downtime (artificer is researching information about advanced technology and its relation if any to magic, another made a pact with a devil and is either going to lean into that or start regretting it). Quests can be abandoned. There is a chasm of difference between the two campaigns.