So my players have just found an iron flask and inside is a Lich. The Lich is going to be the next main plot driving component and I need the players to open it in order to begin this phase. How do I subtlety convince and entice them into opening the flask? Also, would a Lich be powerful enough to do anything from inside the flask? Thanks!
Give them a good reason to open it, deceive them into opening it, or have it opened for them
My players are generally extremely cautious about anything they think I want them to do, especially without a lot of context that give them an understanding of the broader situation around that thing. It can be frustrating, and is not always easily controllable.
If there is a door in a dungeon, they might just barge through it. If there is an ornate, or otherwise unusually interesting door, they might spend an hour examining it only to conclude that the risk is too great and then wander off in another direction. If they find a flask with the words "Open Me!" etched into it, they will most likely abandon the flask somewhere all but inaccessible, or give it to an NPC they dislike.
Organic plot development is great, but when you have an event which must occur then you've settled on a path that is predetermined instead of organic.
So when I need a thing to happen for plot reasons I'll definitely try to get them engaged enough to do it, but I always have a backup plan or two. Ideally the players will choose to open it on their own, out of curiosity or for any other player-generated reason.
If that doesn't seem likely, then they need a nudge. Perhaps the players learn that opening the flask is a necessary element of resolving some other plot point, and the lich escaping is a surprising side effect of that. An NPC is pretty sure they know something about the flask and its valuable contents, completely unaware of how mistaken they are.
And sometimes the players just won't cooperate, so the plot needs to open the flask for them. A thief tries to rob the party, and happens to nab the flask. A fellow traveler on the road gets thirsty, and thinks a nip from the flask might be just the thing but is a bit loose about asking for permission. A royal functionary suspects that someone is trying to poison the Crown Princess, and absolutely will not allow the PCs to leave the flask's contents unexamined. A rockslide suddenly happens nearby, and the flask is bashed open by a large stone.
The bottom line: when you construct a plot point that absolutely needs to happen you do not have much room for player agency, because you cannot abide their choosing not to do it. So give them their freedom of action, but recognize that the flask remaining closed isn't a choice that is actually available to them (whether they themselves open it or not).
Make them an encounter they can't refuse
Per the item description on Roll20,
An Identify spell reveals that a creature is inside the flask, but the only way to determine the type of creature is to open the flask. A newly discovered bottle might already contain a creature chosen by the DM or determined randomly.
If there's a Bard or a Wizard in the party, they'd be able to cast said Identify spell. Either in-character via skill checks or out-of-character by metagaming, they might know that:
You can use an action to remove the flask's stopper and release the creature the flask contains. The creature is friendly to you and your companions for 1 hour and obeys your commands for that Duration. ...At the end of the Duration, the creature acts in accordance with its normal disposition and Alignment.
The list of creatures contained within are variably powerful and variably aligned. Many of these creatures might well make matters worse, but if they're hurt / out of options / feeling lucky, their only option in a high-stakes scenario, combat or otherwise, might be to (figuratively) roll the dice and try their luck with the Iron Flask's contained creature.
Results may vary depending on your players' personalities, the scenario, their character types, their other options, etc. But the best moments in D&D come from when your players need to get creative
There are 2 choices here, 1 which applies RAW and one that requires some homebrew.
The flask is a legendary artifact, so likely somebody in a big town knows what it is. You can have a NPC respected by the characters talking about it to someone when he meets them, creating interest in the flask and possibly having them open it. This example is subtle, but a more heavy handed one could be the same NPC asking to see the flask and telling them to open it, but that could be seen as railroading. They could talk about the power of it (the creature is under their control for an hour) and hint at its lore.
If you would prefer not to do that, you can instead change the flask around a little. Maybe the Lich can communicate telepathically with the creature holding it, or maybe the Lich can try to escape every 24 hours. There are infinite possibilities, and since this one does not require as much subtle hinting and crossing your fingers that the players take the hint, instead maybe even having the Lich cast a spell through the flask to force the creature to open it.
Promise them stuff they want if they do.
You know what the players want- wealth, magical items, fame, fortune, a chance to be good people. Whatever they seem to value. Put an adventure in front of them where there's a large amount of whatever they value, and have the flask promise to solve that problem for them if they throw it. Then, the lich can use their abilities to solve whatever problems for them (likely easily, as a high level spellcaster) and then go do whatever they want to do.
In terms of what it can do, the flask just imprisons the creature. It doesn't say it prevents communication. In theory the lich could talk to those outside and impress on them its value, it's morality, and the power it has to achieve their goals.
Be wary of the risk of railroading.
Players don't like it when you force them to follow a set track. If the Lich does have evil goals, consider moderating them so that the PCs value releasing the lich even if they find out more. For example, rather than having them want to convert everyone in a kingdom to be undead, consider making them an ex king of the area who wants to restore their rightful monarchy and give people the chance to live forever, so that the players feel conflicted about whether to support or oppose the lich.
Be ready for the risk that the players find out and don't want to release the lich. You can pressure them more, certainly, but they may decide releasing the lich is bad. If so you could force them, or you could adjust your plot.