Harry Potter used Liquid Luck to get Slughorn to tell him what information he gave Voldemort. Ginny Weasley also broke up with her boyfriend due to the influence of Liquid Luck.
Was it coercive to use Liquid Luck to get the characters to act in a certain way? In particular, is it coercive to use Liquid Luck with the express purpose of getting someone else to behave in a particular way or to perform a particular action?
Felix Felicis doesn't coerce anyone, and the only thing the potion is shown to manipulate is it's drinker.
Take the very first thing that happens - a jealousy spat from Lavender.
He pulled the Invisibility Cloak over his head and set off down the stairs, Ron and Hermione hurrying along behind him. At the foot of the stairs, Harry slid through the open door.
“What were you doing up there with her?” shrieked Lavender Brown, staring right through Harry at Ron and Hermione emerging together from the boys’ dormitories.
This isn't pulling on anyone's strings. Lavender was already jealous, this is just confirmation of what she already feels. She wouldn't have reacted like that for all 3 coming out, Ron and Hermionie are only following Harry because he was vague and evasive, and for some reason threw on the Invisibility Cloak before he even left the room. The only person's strings pulled here were Harry's, who did pretty much what was needful to set up this exact scenario - lucky for him.
Later on, with Slughorn, there is still no evidence of anyone being forced, or there wouldn't be a need for moments like this:
There was a long, long silence, but Felix Felicis told Harry not to break it, to wait.
Nothing is forcing Slughorn to act the way he does, drunk, morose, and full of regret. Nothing is pushing his reactions through this evening except, to begin with, his own greedy nature, and later, his own guilty conscience. Harry, with Felix's guidance, simply arranged a situation where he'd get plenty inebriated to lower his guard, and then with that lowered guard, honest enough to listen to Harry and come to his own decision.
Is this playing fair? No, and Harry had already tried this fairly. Is this manipulative? Oh yes, beyond doubt. Coercion suggests force, and Slughorn is not forced in any way here. The only person pulled to this result is Harry, by his own desire and the potion.
Felix Felicis does not control others, it just makes the person who drinks it lucky.
“It’s liquid luck,” said Hermione excitedly. “It makes you lucky!”
Harry Potter and the Half-Blood Prince, Chapter 9, The Half-Blood Prince
If the Felix Felicis was coercive like Imperius Curse it would have been completely banned.
“Now, I must give you warning that Felix Felicis is a banned substance in organized competitions . . . sporting events, for instance, examinations, or elections. So the winner is to use it on an ordinary day only . . . and watch how that ordinary day becomes extraordinary!”
Harry Potter and the Half-Blood Prince, Chapter 9, The Half-Blood Prince
There are ample reference in the books that point to the fact that Felix Felicis guides the person to make choices that turn out to be correct (lucky).
“Aragog,” said Harry and Hagrid together. Both Slughorn and Hagrid drank deeply. Harry, however, with the way ahead illuminated for him by Felix Felicis, knew that he must not drink, so he merely pretended to take a gulp and then set the mug back on the table before him.
The Felix Felicis gave Harry a little nudge at this point, and he noticed that the supply of drink that Slughorn had brought was running out fast. Harry had not yet managed to bring off the Refilling Charm without saying the incantation aloud, but the idea that he might not be able to do it tonight was laughable.
Hagrid twitched in his sleep and snored on. Slughorn and Harry stared at each other over the guttering candle. There was a long, long silence, but Felix Felicis told Harry not to break it, to wait. Then, very slowly, Slughorn put his hand in his pocket and pulled out his wand.
Harry Potter and the Half-Blood Prince, Chapter 22, After The Burial
Felix Felicis helps the person who has drunk it, in manipulating others.
I would say No. If you wanted to classity Liquid Luck as coercive then you would have to outright define anyone who is naturally gifted at reading people and knowing what to tell them as coercive. The potion gave Harry the ability to be manipulative but knowing what to say and how to act in order to affect others is not coercive.
