It will generally work, but leans into a highly technical, meta-game style of play. This is not an advantage for players.
First, the basics: destroying line-of-sight, by any means, is generally going to ruin spells which require line-of-sight to cast. Getting an opaque sack with a sufficiently tight weave (an important consideration your players might not consider in advance) over an enemy's vision organs will destroy line-of-sight. So would throwing up a curtain in front of yourself and moving back one space. It works, according to a strict interpretation of the rules.
But it works because of the rules rather than because of any obvious, innate rationale in-game. It's like a long rest healing virtually all injuries: if the rules did not specifically describe that effect, no one would try to use it that way.
It shouldn't be easy. If you decide to allow such a tactic at your table (and you would be well within your authority to forbid it), it should not be an easy-win strategy. Getting the sack onto the lich's head should involve an expenditure of resources (even if it's just time or surprise) and risk of failure with attendant consequences.
If they succeed they get some advantage by limiting what spells the lich can use for some amount of time. That's not unreasonable, as they took some risks to gain that advantage and faced a risk of being worse off if they had failed (even if the consequence is just wasted actions).
It shouldn't be unexpected. Liches are, by definition, not stupid. They are also highly accomplished scholars of magic and are avid magic users. Together, these indicate that a lich will be 100% aware of the possibility and consequences of having their vision affected like this. You would be absolutely justified, in-game, to have the lich be specially aware of this danger (making it harder to accomplish) as well as have some contingency plans to deal with it (making it less valuable even if players succeed). A Legendary Action casting of Mage Hand immediately after the sacking is enough to deal with this, for example.
It's doesn't make the lich easy to deal with. Liches have access to lots of spells, many of which don't require line-of-sight. Some of them might be particularly dangerous for the PC tasked with applying the sack as well. Thunderwave is bad news, and Cloudkill is enough to ruin your day if you'd imagined yourself safe from magic spells.
D&D is a game. Cleverness is great, and I always like to reward it at my table. But the point of a TTRPG is not to trivialize encounters with an "I win" button. Even if everything in the rules lines up to suggest that some tactic should always be effective, if it ruins the game then the DM's job is to change things up. If all the players want is a way to tip the scales in their favor against a lich, you can make up a quest to recover the MacGuffin Sack of Lich Blinding that does so. No amount of clever rule dissection should allow players to skip the game itself.
Wise players should fear this sort of rules-wrangling. Even if some (or all!) of your players are strong experts on the rules, the DM's control of the game world makes "technically-this-works"-style strategies a bad route for them to take. If my players want to split hairs with me for some hyper-specific scenario, I'm very likely to grant whatever it is they're trying to achieve. And then adjust the game world and contents to utterly savage them. They tend not to understand the rules as thoroughly as I do (so my hair splitting tends to hurt them more than their hair splitting benefited them, and more often), and I am totally unconstrained from presenting situations which specifically frustrate their meta-derived tactics.
Players tend to be attracted to tactics like this
At least my players seem to have a real passion for it. My typical approach to this, which I have explicitly explained to my players, is that clever plans and cute ideas certainly can work. As long as I haven't informed them that some aspect of the plan is forbidden they can rely on things that should technically work to actually work.
For a time.
Coming up with a clever tactic or novel solution to a problem is, in my mind, most of what these games are really about. In that spirit, they can get a nice benefit from a tactic that I consider to be cheesing the game at least the first time they pull it off. And maybe more times after it. But, like nacho dip at a party, the cheese just doesn't last very long.
I vary the setup to suit the narrative, but the advantages don't persist forever. Enemy organizations learn about the tactic and eventually respond in a way that nerfs the advantage. Or I design combats where the tactic is less effective or impossible to carry out.
My players have responded well to this. They like it more than simply having their idea banned. And there is some element of resource management to it: if they try the tactic every time they can, then they are a lot more likely to encounter situations where it doesn't work as they intend. It goes from a sure-fire approach to an idea good enough to try, but not to rely on too strongly. If they are a bit more reserved and only use the tactic from time to time they can be a lot more secure in thinking that it will tip the balance when they need it.
What I would do here
I've never had this exact situation, with a sack and a lich, but my players try things like this all the time. I try to funnel considerations about how well the tactic should work, rules aside, into existing game mechanics. So in this case I would lay out two broad options.
If they want to try to throw the sack onto the lich's head, I would treat the sack as an improvised weapon. This makes an attack roll harder to succeed with, and also provides a nice opportunity to get some benefit out of the Tavern Brawler feat (which I always seem to have one player take). I would also be very strict with the throwing range of the sack and with inventory management (once you throw the sack, you'll have to go pick it up if you want to try again).
If they want to jam the sack onto the lich's head manually, I would treat doing so as an opposed grapple, and almost certainly with Advantage for the lich. The lich is not going to just sit there and let the players run through whatever it is they want to do, and as above they would be very aware of this tactic long before the PCs ever tried it.
In either case, the sack is not going to be in place for very long. The lich can easily remove it themselves through a variety of means which don't require an action. The lich can also move out of the area affected by Silence pretty easily, and even if it can't has options that will make that spell hard to maintain (Paralyzing Touch and Disrupt Life are both problematic and available off-turn as Legendary Actions, for instance). I would also be extremely likely to give the lich a minion or two, making this strategy even harder to pull off and even less reliable.
In no case would I set up a combat encounter with a lich and allow the PCs to have a "super easy" fight with such a no-investment tactic.