In order to take advantage of Tibet's better pilgrimage circumstances, the Kailash Mansarovar Yatra from Lucknow is often conducted from May to September. While the nites are still chilly during these months, particularly around Manasarovar Lake and during the Kailash Parikrama, the daytime temperatures are often tolerable. https://holykailashtours.com/trip/kailash-mansarovar-tour-via-lhasa