Windows 10 Slow with LG Monitor

Do you know the specs of your Yoga 2? I'm going to theorize that you got a relatively cheap one, but I believe they all use the ultra-low power intel CPUs (Y-series). The CPU is responsible for rendering every pixel on your screen, and adding the second monitor adds considerably more pixels to render. Possibly more than double if your Yoga 2 has only a 1366 x 768 screen, as I assume the monitor you connected is 1080P or more.

You may not be doing much on the machine in terms of graphic intensity, but the iGPU in those ultra low-power CPUs are designed to be adequate for the basic tasks you'd do on a single-monitor general use laptop.