Lords of the Realm II is one of my favorite games. I've been waiting 20 years for something similar and haven't really found it (LotR III was different and no good), unfortunately.
The Stronghold games are awesome and could very well interest you, but might not be quite what you're specifically looking for. They're much more real-time strategy and it sounds to me like you're after a turn-based, macro-level strategy game. LotR II had both parts, but the main and best part and what you seem to be describing is the turn-based part, in which you conquered adjacent counties on the map one by one and attempted to hold them (against enemy players and internal revolt because you mismanaged the economy and happiness). Edit: As an aside, those who love the Stronghold series might care to look into
Cossacks 3, which I haven't played yet, but which is getting a lot of praise.
The closest games to what you're after that I can think of are
Crusader Kings II,
Europa Universalis IV and
Civilization VI. CK II is pretty historical and focused only on the medieval (like LotR), but is very complex, has a steep learning curve and is heavy on politics and religion (not so much economy). EU IV (from the same developers as CK II) is pretty historical, but is also very complex, has a steep learning curve and is not focused so much on economy. Civ VI has the casualness, approachability and balance between warfare and economy of LotR, but is not strictly historical or constrained to the Medieval era. Any could probably scratch some of that LotR itch, though not all of it.
I would look into those games. I, personally, would lean toward Civilization VI as having the closest "feel" to LotR and because what you're looking for--"Warfare. Economy. Strategy. Regional domination"--is exactly what Civ is all about. Of course, you probably know all about Civ, have played it before and are just seeing if there's anything else that's more like LotR, but, as a LotR fan, I can tell you that I haven't found it. The Civ series is the closest that I've found. You may be able to tailor it even more closely, though, through the use of mods. I wouldn't be at all surprised if there's a mod that limits the scope of the game to just England during the Medieval era. You might look into that and even buy Civ V, instead, if such a mod exists for that (since Civ VI just came out and mods are no doubt very scarce still compared to the very mature Civ V).