Will this work for a Lenovo laptop?

I want to be able to run an external GPU like this:

Will it work with a Lenovo laptop?

The brand of laptop has nothing to do with it.
External graphics has been around for a long time.
USB, VGA, Ethernet are not compatible.
HDMI is output, not input.

There are some laptops with SATA Express, and there are probably ways to connect by adapters after removing a DVDRW through SATA. On one method they connect internal to the laptop by removing the back and leaving it off either through an M.2 slot, or mSATA or replacing a wireless card with an adapter.

You would need a graphics card, external 12Volt power supply, a purchased or home-made rig and a suitable laptop junction. They show an old business level Dell. If you have a Lenovo Thinkpad with an external card slot you can hunt around the web for the hardware or instructions.
If you want to turn a laptop into a desktop PC as a major project you can do that also.
It is much better to learn how to build a tower PC and save up the necessary money and have a wonderful gaming PC. Laptops make bad gaming. Even a GTX 960M laptop is only about a desktop GTX 750 TI US$100 card.

State your exact model of laptop and you can be pointed in the right direction. What you see is mostly a curiosity as someone testing something or a project guy that likes to tinker with things.