First of all, I like it.  I like it a lot.  One of things that distinguishes FE from other similar games is the role-playing element, and with LH I think this aspect has been strengthened.  That said, here are some thoughts:

1. I loved the Ascian quest.  Please add more of these random quests - they really spice up the game.  But speaking of Ascian, please give her better movement in combat.  She rarely got to use her special ability because by the time she trudged up to the front, the fight was over.

2. Archery seems too weak.  Perrhaps it was just my style of play and the races I encountered, but archery units never seemed to do double-digit damage.  I ALWAYS had a few warg archers in my armies in FE, but after a few games of LH I gave up and went to pure horse lancer armies.  The archers were just taking up space better used by others.

3. I agree with others that the Warrior path seems weak.  One thing I would have liked to have had in the Warrior level ups is increased moves.  As noted above, I tend to use cavalry a lot, and most battles the heroes had trouble keeping up, even when they were mounted.  It meant that all their cool weapons and abilities were often wasted - they never got a chance to use them before the combat ended.    

4. I can't recall if this was true as well in FE, but the colors were awfully similar in LH, especially orange and blue.  I could not tell the cities and outposts apart.

5. Finally, will you please for the love of god add some way to select units while they are in a city.  I finally learned of the "v" key, which will put them all outside.  But sometimes you want to just send some, not all, and having to use Ctrl-click to select each unit is a real pain the butt.  I recently started playing Master of Magic again, courtesy of GOG.com, and that game, old as it is, had a very easy way to do this: click on the city, all the units appear in a large box, and you select or deselect each one before giving the move order.