I know @finarvin mentioned once he had GMed LotR with the Amber rules, but that it was a so-so experience. I have used Amber, my beloved Amber, for all kinds of genres and settings, but not for Lord of the Rings...
Yeah, the biggest problem is that Amber Diceless is designed to work well with cinematic adventures, where plot runs superior to the nitty-gritty. When I ran my Lord of the Rings game with ADRP I ran into issues when we had our first encounter, which was a band of orcs outside of Bree. We got into a firefight with archers and I could have adjudicated something like this with D&D or similar system just fine, but the notion of counting arrows and hit points just runs counter to the way I typically handle Amber Diceless.
Fundamentally, a lot of the ADRP elements would seem to fit Middle-earth. Characters have POWER which is a lot like Psyche. The basics of sword or axe combat are represented by Warfare. Grappling and lifting are Strength. Endurance is Endurance. The part that threw me the most was archery combat and what that represents in terms of game mechanics.
ADRP attributes start at -25 but my scale starts at zero. Attribute scales something like this:
0 = Normal (compare to shadow at -25)
15 = Exceptional (compare to Chaos at -10)
25 = Supernatural (compare to Amber at 0)
125 = Mythic (around Ranked-100)
I've tried various scales and have never been 100% happy with them, but the actual numbers aren't as important as the relative numbers. I have some MERP (Middle-earth Role Playing) sourcebooks from the 1980's that stat out characters on a 1-100 scale and provides a conversion to 3d6 for the D&D fans. There are also rules for First Age Eldar going above 100%. If I try another Middle-earth Diceless I may try that scale instead. The advantage there is they have statted out creatures as well. If I go with a 3d6 scale I might tap into 5E's Adventures in Middle-earth, since AiME also has statted out monsters. So many options.
One key here is the assumption that (unlike in ADRP) not all characters have the same number of points. If a party has a hobbit and a high elf and you try to give them the same points to work with the results get pretty gonzo, so highly variable group types only work if the players are willing to play roles and not be point munchkins.
With this in mind, a typical human or hobbit could be somewhere in the 5-15 point range, elf or dwarf more like 15-25. Clearly this is up for some interpretation. A Numenorean (high man) is closer to 15, a regular person closer to 5. High elves (particularly in the First Age) would be 25 or higher.
ADRP's Shape Shifting works well in Middle-earth, and at a cost of 35 is probably priced well. (Unless you decide upon a d100 scale like in MERP.)
Magic use should probably be priced around the same point, with the caveat that Middle-earth magic tends to not be the flash-bang sort but is mostly subtle and mysterious. (Somewhere I have typed up a list of Gandalf's spells from LotR and can post it if there is interest and if I can find it.) Another point of emphasis is that magic use tends to attract the attention of the bad guys -- orcs, Nazgul, perhaps even Sauron -- and so doing magic can be like lighting a bright torch at night and should be somewhat restrained. Therein is the tricky part, a sort-of check-and-balance for diceless spellslingers.
I'm sure I have more notes laying around somewhere.