I noticed a few other people reported this problem so I thought I'd move it here for those who aren't looking at the game now that the giveaway is over.
When I clicked the custom cursor button, the lag disappeared and the game is so much better. It seems that there's a few problems that the custom cursor fixes so if you have a problem, click that and see what happens.
It's a great game so I hope this fixes if for you. The lag was so frustrating and I'm sure that not being able to see the cursor is too.