Marks and Sky short answer yes this is lag is normal.
Long answer GC4 is a graphics hog.
The consensus is that the two main problems is a player's graphic settings, Marks you seem to have lowered yours I have a NVidia 2070ti graphic card and have lowered my settings to minimum and still can get lag though not much.
The second problem is that the AIs build ships then more ships before they build more ships.
This in and of itself would not be a problem and only marginally effect turn time.
Except the AIs do not put these ships into fleets but keep them separate. The Devs have changed some code to stop this however as far as I know it will be in the next test update not in the current 1.10 test version.
Again, this in and of itself would not be a huge drag on turn times.
The next leg is more of a problem the AI seems to move each and every ship each and every turn separately.
This third leg when combined with the other two is what most believe is causing the problems.
There are two things you can do to speed up your turns that appear to work for me.
First turn off following both your and the AI ships, this will limit the graphics from rendering every hex moved and the ship moving through it.
Second zoom out till the pretty little ships and planets and whatever turn into icons. This allows the Graphics to render very simple symbols rather than the sophisticated ship and planets.
I too am not happy with some of the bugs still present I do not have appreciable lag times myself I however have a top rate Gaming Computer and have set up the graphics and other settings as I mentioned above.
