Sometimes you just want to throw a curveball to your players or see them out of their comfort zone. Here are three ideas to do just that. The first puts the players in the role of stopping the main character of your average Lovecraft story from finding out the truth and revealing horrible secrets the people in power want kept secret (basically they have to become MiB), the second makes the Lovecraftian entity into the victim of a mortal, for the first time (being alien and weird doesn't automatically makes you invincible, who knew?) that needs to be saved, and the third turns the players into a special force tasked to stop the good guy from winning and destroying the balance in the process.
1- Strictly Confidential Questing
Horrible, unspeakable things lie beyond the stars, hidden in demented dreams or crawling between the shadows at the corner of your eyes.
And the people in power would really like those things to remain hidden. The local government knows pretty well they exist, you really think they never bothered to check the basement of that creepy asylum or the abandoned church? They know about the elder gods, as do the angels and other protectors of life and order. They keep those things hidden from the populace, to avoid panic or the birth of crazy cults or wars against madmen trying to take control of those alien entities.
The players are hired by a king, spymaster or a powerful planar entity like a celestial or someone from mechanus to keep the elder gods hidden. They will have to stop an investigator or a group of them from finding out about a cult of Cthulhu, or maybe a bard from writing a book about his bizarre, alien dreams.
Basically, the players are in the opposite of a Lovecraft story: they are stopping the protagonist from investigating and trying to keep everything a secret. Obviously, they can't just kill them, they have to try and mislead them or convince them to give up, but it won't be easy. If you want to include more fighting, they could have to fight the cultists that they are "protecting" as they're not the most rational people, or some elder creatures trying to get the investigator to see them.
"Why don't they just destroy the cult?" you may ask. Because there is no point: it's already been tried, new cults just reform in new places, as the alien entities visit our world to find servants. This cult is well controlled and kept secure, their rituals interrupted or ruined before they can do any real harm. Basically, they are a contained infection, and it needs to remain a secret.
2- And with a good shankin' even death may die
A mad man invoked horrifying things from beyond logic and reason, with perverted rituals he called forth an alien monster, an abominable thing whos mere sight can send anyone mad.
Then he passed his wisdom saving throw, so he stabbed the thing in the face. The thing is currently hiding in the man basement, trying to escape, before the man can murder it and absorb its power or use its body to craft items.
The thing contacts the players through whispers or their dreams, asking for help: they must protect it and find a way to send it back to its dimension before the madman takes its power.
Obviously, it's still an alien entity, it could have troubles talking with them or making them trust it, and its simple presence could deal damage or cause mutations to the players and the world itself. Still, it needs to be saved before it is killed and devoured.
How often have your players had to babysit an old one? They may have to push a gnarled mass of tentacles through a portal as mouths appear in the floor and try to eat them (sorry, the alien god can't help it, it just happens, sorry again) or they may have to pour a pool of sludge inside a portal, but every time they touch it they mutate or risk losing sanity, meanwhile a madman (and his minions) fight to get inside and absorb the thing. As long as the thing is in our world, the madman is linked to it and is rendered almost unstoppable, he's already syphoning its power.
3- When there's no more room in hell, the dead will walk the earth
A great hero was born, they rallied an army of paladins and celestials and marched against hell itself. AND THEY WON. They are currently trashing the upper layers of hell, laying waste to the devils and their cities.
Little problem: the millions of souls and devils that were there are flooding in the material plane, as their plane is being literally destroyed. But the heroes don't care: no sacrifice is too much, losing the world to destroy hell is more than worth it in their eyes. A heroic sacrifice is needed.
The rest of the multiverse disagrees. But the devils can't just team up to fight, their laws and contracts are so complicated, they can't easily go into other circles of hell to fight, and would take a long time to organize. On the other hand, the angels consider these "crusade" an insane and heretical act, but they can't do anything about it because A: It's in the middle of hell. B: technically the crusade hasn't done anything "wrong". Angels aren't allowed to just go there and butcher other angels, they too have their laws.
You know who can? Mortals. The players are hired by a joined group of devils and angels to go into hell and stop this excessively zealous army of celestials and paladins from destroying the world. They will have to fight with some devils, as many are more than happy with the current situation, and angels at the same time, while other devils and angels support them. What a weird and confusing situation.
With a mix of diplomacy, subterfuge, intelligence and combat, the players have to reach the battlefield in hell and convince the crusaders to stop. Some can have some sense talked into them, others will sadly have to die. All for the greater good.
And once its all over, who knows what the repercussions will be, and how the players will be judged by both factions for their actions?