I just checked in the first major LH-specific AI update.  Players should notice a pretty significant improvement.

I fixed a pretty obnoxious bug with regards to city leveling which was absolutely crippling the AI mid to late game (the effect was that city level choosing ended up largely random).

But overall, a few thousand lines of code were either written or modified with LH in mind.  It'll be interesting to see the effect others see.

What I was able to see was mostly in the late game where the accumulation of "poor choices" the AI made led it to becoming largely petrified. If you were a human player and could just hang in there, you'd ultimately win IMO.  This usually was most obvious when looking at the graphs.

Also, it now matters a lot more which players you go up against. They now play fairly differently from each other.  It'll help when they have more unit designs to choose from.  

Assuming progress is being made, I'll be happy to keep doing more on this angle.  I think there's a lot of low hanging fruit in there.