Can an MSI Geforce GTX 1060 6gb fit in my case?

So -- measure the space by opening the cube and then look up the size of the gtx 1060

what's so hard about that?

The Lenovo product page has a review that says:
" Mine has a core i5-7400, 8GB UDIMM RAM, 1TB HDD, AMD 570 4GB graphics card…"

So that might be as large as the one you want to put in.

I suggest either waiting for the next Generation of Nvidia cards or saving up more for a better card because going from a 4gb RX 480 to a 6gb GTX 1060 is a sidegrade. By the time you have the extra $100 saved up, the new generation of cards might already be available.
In some games the RX 480 or 580 does better but in others the GTX 1060 does better. A GTX 1070 would be a meaningful upgrade. The only reason to look at a GTX 1060 is because you have a reason to use the CUDA capabilities for GPU acceleration that help with some video editing programs.

A reference RX 480 is a dual slot card that's around 2" thick, 4.5" wide, and right around 10" long. I have 2 of these cards.

Asking about an MSI GTX 1060 is vague because some models like the Armor or Gaming X are around 5.4" wide x 11" long, but other versions are nearly the same size as the reference RX 480.

To be certain, you will have to measure inside the case where your existing RX 480 is located.

And, if you have a Freesync capable monitor then going with the GTX 1060 would almost make no sense at all.

Going from a 480 to a 1060 isn't really an upgrade. In some games, you will probably see a slight (<5%) performance increase, but in others you will probably see a slight performance decrease.

If you worried about the card fitting inside your case, i would suggest aim for a 1060 small form factor based card (ITX).

Yup, this is one of those situations where you're just gonna have to take a ruler and measure it. Any card seller worth buying from will list the card's measurements.

And before you buy GPUs, compare their benchmarks to make sure you're purchase is worth it. Websites like these are good to check