Greetings!
The RX 460 should fit in the PCIe slot that is available on the motherboard, and could potentially work just fine as long as you get a variant that does not require extra power connection from the PSU. Here is an option:
https://www.newegg.com/Product/Product.aspx?Item=N82E16814137028#close
The concern howerver, is that your computer has a PSU that is probably around 280 - 300 Watts. Some RX 460s are an 84W card, but can ramp up to over 100W under load. Here is a link to a test, but this was with a card that required an extra 6 pin connection from the power supply:
http://www.tomshardware.com/reviews/amd-radeon-rx-460,4707-5.html
This is a bit of concern for your power supply may not be able to power the card sufficiently. The variant that I listed above will pull less power than a variant with the extra 6 pin connection direct from the PSU, but I can not find specifics on load draw for that specific card. I also can't see an extra connection from the PSU in the Lenovo to allow for the type that requires the 6 pin, which is common for OEMs for they design the components together and rarely provide a PSU that can supply more than the original system specs and hardware require.
Chances are it will work with a PCIe powered variant, but you may find your PSU underpowered at load, though this is only a possibility and may not be the case without being able to math out the load requirements of all the components in your system. By my estimates (and this is an estimate based on your computer's specs and standard approximations of component draw [CPU, RAM, HDD, case fans, etc]), your system is pulling around 155W at load...A PCIe powered card can pull up to 75W from the slot, so the GPU is limited at that maximum. Add that to the 155W and you get ~230W of draw at full load. This is creeping pretty close to your margins for your power supply. A common wattage for Lenovo computers at that time were around 280W, but they are not high end units and may not be able to provide that much in a stable manner if at all, so there is the potential issue.
Looking a little closer though, it appears Lenovo used a standard PSU to Motherboard 24 pin connector, so if you find you need to upgrade your power supply, you should be able to without too much issue.
I really hope this helps!