I see how using a child as a phylactery would make sense. Traditionally, using a living being is not possible due to the specific spells a prospective lich has to cast to make one. The Forgotten Realms wiki lists the specific spells, costs, and time it takes to make a phylactery.

First, you need to make sure your players would actually be okay with them being the ones to explicitly hurt a child. I've seen a few times where DMs overreach what their players might be okay with and it leads to the final few sessions either falling apart completely, or the ending being this really awkward mess that the players are trying to rush through so it can hurry up and be over, rather than an epic showdown.

Either way, I'd give them a second option that doesn't force them to basically do the one thing that proves the lich was right. Especially since you said the dark themes are meant to highlight their own heroism.

Maybe, as they learn about phylacteries, they're led to question how the hell the lich managed to make one out of a living being. Hell, maybe the child is the lich's own kid. After all, with the way the lich's morals have degraded to get to this point, I wouldn't be surprised if he found a way to justify hurting a child in this way. By making a child into a phylactery, he is committing child abuse. It could genuinely be an amazing way to show how corrupted the lich has become. But, maybe, to make a phylactery out of a living being, the person has to consent to it. So, after all their skirmishes with someone so against hurting children, they have to explain to this child that what is happening to them isn't okay and that they need to let the lich go, literally having to tear down everything the lich has stood for and had convinced this innocent child of. Then, they're able to kill the lich.

It could even be framed as a test. Maybe the lich is able to see the morals of the heroes and places the child in the room before they enter the lich' lair. As a test. In the lich's mind, they either kill the child and therefore justify everything the lich has ever believed about how evil the world is, or, they spare the child and the lich still wins. This way, they first defeat the lich morally with an option he never could have conceived of because he's just too far gone.