Humor is one of the most difficult things to handle well. Sprinkling your script with sparkling one-liners sounds brilliant and hilarious, but works better in a setting that is meant to be comedic.
A film like the Princess Bride can rely on throw-away one liners (Fezzik: "It's not my fault being the biggest and strongest; I don't even exercise."), running jokes ("Inconceivable!", Fezzik's rhymes), physical humor (Westley falling down all the time after being mostly dead - "Gently!"), unexpected answers* ("With all dead, there's only one thing you can do - go through his pockets and look for loose change." "The most famous is 'Never get involved in a land war in Asia,' but only slightly less well known is this: 'Never go in against a Sicilian when death is on the line.'"), mispronunciations ("Mawwadge")....and basically every different form of humor, because it is a comedy. Sure, it has its serious moments. The repeated 'Inconceivable!' gives way to the repeated, 'Hello! My name is Inigo Montoya! You killed my father. Prepare to die!' But the audience is meant to spend most of the film laughing, giving more weight to the "As You Wish" moments.
We...have to do the opposite. Take the inexorable weight of the tragedy that is the Silmarillion and lighten it with character moments that will just make the audience weep harder later. There are films that are unrelieved in their seriousness/horror. The humor is used very sparingly, and more poignant than laugh out loud funny. The Passion of the Christ doesn't have a lot of light moments. I mean, there's about 2 hours of bloody torture, so even flashbacks where characters are having a normal conversation and no one is in pain or covered in blood seem jarringly idyllic. But there is one light moment that gets a laugh - a flashback to Jesus-the-carpenter building a table, and his mother expressing doubts about the design. He explains that it is high enough for chairs, and she says "It will never catch on." The scene most likely to make the audience cry? The flashback of Mary running to help toddler!Jesus interspersed with Mary running to Jesus who has fallen while carrying the cross. The audience is invested in her as his mother, and the earlier scene helped to set that up.
I have not seen U-571, but I've been told it is intense. There are films that deal with dark topics and still manage to inject humor. Jakob the Liar is a tragi-comedy set during the Holocaust (Warsaw ghetto) featuring Robin Williams. A much better comedy set in a WWII concentration camp is La Vita Bella (Life is Beautiful). I mean, the Silmarillion is dark, but it's not actually genocide/torture dark for most of it. There are a few scenes like that, and the story of Túrin is *all* tragedy - but we have the Frame to handle that. If the frame is Aragorn out adventuring in the Wild, we could have running jokes throughout the season there. For instance, Halbarad could take every bad situation they get into and say something along the lines of 'it could be worse...' and then it gets worse. Beleg could do something similar *once* in the main story, and it might be funny at the time.
The trick is not to be tone-deaf, and not to force the humor if it doesn't work. Allowing for some light-heartedness is not the same thing as having a Jar-Jar character. I mean, C-3PO fulfilled the same role in the original Star Wars trilogy, by always being afraid and misunderstanding....but he was tolerated much better by audiences. Do we need comedic background sidekicks, like the guards in elf-king's cellar in the Hobbit? Minor side characters who make foolish mistakes? Or just are at the mercy of the decisions made by higher-ups? I would prefer to give all characters their dignity. Saeros is going to have an ignoble death, as is Salgant of Gondolin, so it's not like *all* of the characters will be noble and heroic. But I'd rather not have a 'I am only here for comic relief' character - those are annoying. We're not making a children's show, and even if we were, Bebop and Rocksteady are annoying in Teenage Mutant Ninja Turtles and Bulk and Skull are annoying in Power Rangers. Please let's just not.
* The term I was looking for was paraprosdokian: A paraprosdokian is a figure of speech in which the latter part of a sentence or phrase is surprising or unexpected in a way that causes the reader or listener to re-frame or re-interpret the first part. It is frequently used for humorous or dramatic effect.