What's the best graphics card you could put in a Lenovo X240s Laptop?

You should go with Genuine Dell NVIDIA GeForce 8600M Video Graphics Card For Vostro 1500, 1510, 1520 Inspiron 1520, 1521 Laptops Part Number: UW390.

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The Lenovo X240 is not designed to have a dedicated graphics card. It uses the video circuitry built in to the CPU to operate. So it can't be upgraded like a desktop.

Get a desktop.

None whatsoever, all of that range use integrated Intel HD4400 graphics which are built into the processor. Changing the GPU is almost exclusively something that you do with desktop computers, not laptops.