Köl Suu lake is located 12 km from the Chinese border. Even though I’m a Chinese national, I still need a border permit to visit the area. My local Kyrgyz driver later told me that even for Kyrgyz nationals a permit is needed (don’t know why). Anyways, to get it you can arrange it with the only a few tour companies, CBT or Kubat tours, in Naryn or some other tour companies in Bishkek. The border permit costs around 1800 som (~€20) with Kubat, you can have it arranged in advance or show up in CBT office and get it after 3 hours.
I found the driver through Kubat. Unless you ride your own horse, motorbike or SUV, it is difficult to get to the lake on your own because the road is unpaved and many parts are quite difficult.
driver asking the shepherd guy if we could stay in his place