Without a permit travel to any part of Nepal, it is illegal. In the same way, the Gokyo lakes are in Sagarmatha National Park, which is a UNESCO World Heritage site. Thus, to travel or trek around the park, you’ll need a TIMS and Sagarmatha National Park permit. The TIMS permit cost you around USD 10 per person while the Sagarmatha National Park permits cost you around USD 30 per person. The permits are available in Kathmandu and your Sagarmatha National Park permits are in Monjo. In case you are traveling with the agency then they will provide you with it.