I am surprised that no-one else seems to have picked up on this RPG yet. I was recently just surfing the net and came across this post
http://batintheattic.blogspot.co.uk/2018/01/why-middle-earth-has-been-working-for-me.html on the Bat in the Attic blog that I follow intermittently.
It has a brief overview of a relatively new setting for Middle Earth but rather than a tabletop battle game it is an RPG based on the D&D 5e rule set (on an OGL licence). The game is based in the 60-70 years between the Fall of the Necromancer and the destruction of the One Ring in an area called The Wilderlands. It is a low magic system that is more character interaction driven than outright D&D hack and slash, and seems really good (only read the rules so far). The main point for me is that it is based on the books rather than the films, but it allows any interpretation of Tolkien's world you wish.
A quick trip to Cubicle 7's webstore
https://www.epayments.co.uk/epages/es113347.sf/secde972b9bfc/?ObjectPath=/Shops/es113347_shop/Categories will show you all the rulebooks and supplements to date (plus their porevious system is also compatible).