Did factory reset, attempted to flash CWM using SP Flash Tools and fastboot but to no avail. How to unbrick Lenovo A316i than?
I spent another few hours trying things, and ended up going to a friend who had Windows on PC, with this guide: Lenovo A316i Stock Firmware - xdafirmware on this site placed archive which had everything needed in it:


Unmodified stock firmware which doesn't require modified Recovery
Lenovo USB Driver executable
Smart Phone Flash Tool 3.x (probably 3.1336 I didn't watch concrete version)


And guess what? I managed to install driver and flash firmware in matter of minutes, and got phone booting fixed!

P.S. So, the solution is to use 3.x SP Flash Tool and right firmware, but since 3.x isn't runnable on GNU/Linux, well you have to install windows first!