I have recently installed Debian GNU/Linux on a Lenovo V510. It got working almost out of the box (I explain below what needed fixing), and everything seems to be running now. I experienced random freezing of the machine at first, but the issue seems to be solved (see below).
Installation I did a net install of Debian 9.1 (stretch). In the BIOS screen I turned off secure boot and set boot mode to UEFI (no BIOS compatibility).