Hey Asfolas, welcome to the forums!
The lag that you speak of really does depend on the power of your computer - and unfortunately, that lag is gonna increase considerably once my updates have been added to the official release.
The amount of content that we are ading to the game is massive, and all that info needs processing power. More stuff means more power - or more lag.
HOWEVER, the game is still far from complete, and has undergone little to no optimisation. That means the game may not be using the power available to it as efficiently as possible, so some - perhaps a lot - may be being wasted. Until this is done though, we honestly won't know how much improvement can be gotten from the game. Optimisation will be one of the last things done to the programming to ensure the entire game is optimised though, not just part of it. This means you'll have to put up with lag for the time being, but i'm sure things will be better in the future.
Just out of interest, what are your system stats, (CPU, RAM, Graphics, etc) and how long is the turn lag? Info like this can help Mike (The developer) find if there are any incompatibilities etc that may be slowing down the game.