I was in Tibet 10th-19th of June, 2017.
The link below is the travel agency with whom I had a really great 8-day tour in Tibet.
Best time to go to Tibet is from May to October, this is also the busiest time in Tibet.
Best months to camp in Tibet are May and September when it rains the least and the temperature isn’t too cold.
The peak of Mount Everest will be more probably hidden behind clouds in April, May, September and October.
Tibet Entry Permits aren’t typically issued in February and March, when Tibet is typically closed for foreign travelers for 5-6 weeks. In early April Tibet reopens for tourism.