I picked up FE:LH again with the advent of 1.3 (already made my kudos post) and there's a few remarks I have after the first 2 and a half playthroughs.
I play on Challenging World - Opponents, large random maps, -1 technology rate (meaning one less that default), +1 quest occurrence (meaning one higher than default). I play a custom race/hero, which probably means I am a bit more powerful than a default race. I have all 3 DLCs.
First two games, I turned off everything but Conquest win, and quit when it was clear all that was left was to steamroll what was left of the AIs. Can't say it was easy to get to that, but it wasn't very difficult either, it was definitely interesting playing though. My overall impression though was that I was fighting against wildlands mostly, the AIs just happened to be in the way. Maybe it was because I only left Conquest so I didn't fear anyone go for the other wins though. Didn't use gamey tactics, but I did reload a few times, mainly intentionally when I tried to see if I "could beat that ridiculously big monster there". The third playthrough is underway but after 100 or so turns I am in the lead consistently (I have all winning options on this time though).
So in that department, the AI needs to get smarter (yeah, yeah), but at least they are interesting. One thing that stands out is that I think they are not actively hunting monster spawns and/or lairs. I can't say for certain, and I am certainly biased since as soon as I spot something I beeline for the "XP pinata" but I think the AI is not doing that, meaning they miss out on leveling up their heroes and troops. They only seem to care about what's inside their borders and enemies just outside them, are ignored even by more powerful AI troops that could just go for the XP. I think most of their leveling comes from fighting each other. That is not to say I haven't seen them attack monsters, it's just that there's so many of them loitering around their lands as opposed to mine.
I like the new hero system and trees are interesting and fun, but I think heroes should be a bit "cheaper" to get, maybe at 75% the values you get them at. I rush to do all quests as soon as I am able to, even sacrificing leveled troops for it and rush to clear lairs for the +1 fame, but still, I would like to have a couple more heroes. I chose to have henchmen in my custom race especially to alleviate that. I don't know how making them cheaper would affect the later game though with all the city improvements that grant fame per round. Maybe it's just personal taste.
I think technology should be at default a bit slower (maybe where the -1 is). The reason is that if I leave it on default, my cities never stop producing improvements. If I factor in building on resources, the queues just feel like a prioritization of a never-ending list instead of actually improving the city. You just don't get to feel the impact of an improvement on default. Let alone fortresses which have to build units as well... With the implication that fielded units are never completely up to date except much later in the game.
Does the autoresolve system take into account anything else than hp-att-def ? I can't tell for sure, but I think that it does not. Maybe, and I know this is a lot of work, you should try and extrapolate abilities to modify those (ie, heal spells add to hp, attack spells and initiative abilities add to att, stoneskin spells add to def, etc). Again, I can't say for sure, and I rarely autoresolve (kudos on that too), but I think that the autoresolve as it is, hampers the AI even more.
Combat is very nice. I only resort to autoresolve on hopeless fights or easy ones. Most of the abilities and spells have their uses and are good to have, heroes are a force to be reckoned with, and... very nice, indeed. It is still possible to cheese your units but I prefer a rich system where players decide on how disciplined they will be instead of a limited, "fair" system. My only gripe are the rewards (combat and lairs). XP is fine but maybe instead of the 100th dagger that drops we could just get plain gold ? I know I can sell it, but still. Maybe replace some of the mundane stuff with just gold.
I won't go in to the diplomatic aspect of the game since that is being currently revamped.
Lastly, I can't remember very well, but in EWOM and/or FE it was mentioned that the AI would "learn" from unit builds the player used and would copy them in subsequent playthroughs. And I think it was suggested that the player should play a game with each faction so that there would be a "pool" of builds for the AI to have some efficient builds to choose from ? Is this still in FE:LH or am I just turning senile and don't remember well in my delicate age of 40 ?
Anyway, all that being said, I am very much enjoying the game now. I expect this to get better and better with every patch, and I hope there is an expansion in the works.