I have a Surface Pro and I had the same problem: Bluetooth (Microsoft brand) mouse LAG while downloading from internet big amount of data (video or many web sites downloading at the same time).
I was able to fix the problem today by removing the mouse device and pairing it again.
I don't know if the problem will come back or not (it is working well just from today).
THE PROBLEM IS BACK AGAIN: mouse cursor lag move while downloading video or several web pages at the same time from internet.