Between the 17th century and 1959 , the Dalai Lama was the head of the Tibetan government . During winter , the Dalai Lamas stayed in the Potala palace . Starting with the 5th Dalai Lama and until the 14th Dalai Lama 's flight into exile during 1959 , the Dalai Lamas spent the winter at the Potala Palace and the summer at the Norbulingka palace and park .