You cannot really separate setting and system. For example, the D&D system uses [Vancian magic](https://tvtropes.org/pmwiki/pmwiki.php/Main/VancianMagic). That isn’t how magic works in Lord of the Rings. So you cannot „see Lotr through the lens of the D&D system“.

I completely agree that system can influence the setting; the entire point of playing different systems with our setting is to see how those systems impact our world building. The very act of playing a dnd game in the setting of middle earth is seeing it through the lens of dnd!

Dungeon Crawl Classics. The rules are fun, but still quick and light. Combat is deadly. Magic is powerful but can cause mutations if you’re unlucky. The modules are fun, and allow you to build a world around.

Worlds Without Numbers is pretty great and have a lot of tables to help flesh out everything

I quite like Monte Cook's Cypher System for just about any setting. Fast, elegant rules with just the right amount of crunch to keep things interesting. It's really easy to grasp and can be easily tailored to fit any setting. I also love how it uses a descriptive sentence instead of cookie-cutter character classes.

Absent knowing anything else, and assuming most of the "usual" fantasy tropes are in place? Either Savage Worlds, or Colville's Draw Steel depending on how I feel and how my upcoming experimental play of the second one goes.

Quest Worlds. It handles all conflicts the same, whether they're a combat or a heated debate for the party's life. What determine if you go into an extended contest (ie combat) is the importance of the conflict, not whether weapons are involved. Additionally, relationships and social status (for example) are handled as skills are and can be used to reinforce other abilities, so a warrior fighting to save their family will really fight harder. This makes relationships, social status, etc matter in terms of rules and bring the rp and rules into alignment. The abilities also scale, so that a master fighting a novice well have an overwhelming advantage.

So you’re looking for discussions like: Is Gandalf a wizard, sorcerer, or cleric? Which level are his spells? Sounds like fun.

My favourite is Burning Wheel from the same devs.

Burning Wheel hands down. -"Artha" system for codifying character goals into skill development. Characters pursuing their goals is the primary means of progression. -Lethal and unbloated combat. -Many types of magic with very diverse play styles. -System for resolving in game in character arguments that tie into other systems. The whole system is very thoughtfully produced and the systems all relate and tie back to Artha and character development. The setting is very pulp/dark fantasy. My playgroup will be returned to the game soon and offer for years to come.