When Tibet was invaded by China, the Dalai Lama went into exile because he--being the leader of Tibet--was viewed as a threat to Chinese authority. He felt he could better help his country if he was free.
To be honest there is no such thing as Dalai Lama religion. The Dalai Lama between the 17th century and 1959 was in fact the title of the head political figure of the Tibetan government as well as the country's foremost religious figure. The current Dalai Lama is the 14th Dalai Lama in the line. However, each new Dalai Lama is chosen as being seen as a reincarnation (born again) of the previous Dalai Lama. The religion you may be thinking of is Buddhism; the religion practiced by the Dalai Lama and his followers.
Headed the government
The Dalai Lama escaped persecution when China invaded his country, annexing it permanently. His followers begged him to go into exile in a safe country.
The Chinese Government.
The Dalai Lama is supposed to be a reincarnation of the other Tulkus. The Chinese government uses a number of criteria to find the next Dalai Lama. They look for crows nesting at certain house and follow clues given by the previous Dalai Lama.
India
His Holiness the 14th Dalai Lama of Tibet's name is Tenzin Gyatso. But he has decided to step down. If the government excepts this, he will no longer be the Dalai Lama. He thinks that it will strengthen the government and modernize it. I will be sad but I respect whatever he decides!
The Dalai Lama is the secular head of the Tibetan government in exile and the religious leader of the Gelug lineage of Tibetan Buddhism.
India
Tibet thanks
The Dalai Lama is seeking to split Tibet from China. Chinese Gov't wants to retain the military strategic significance of the Tibetan Plateau (perfect location to protect against nuclear weapon countries like India and Pakistan), Oil resources, Secure it's boundaries, cannot let one territory become independent for fear of becoming another USSR AND the untapped natural resources of Tibet.
The Dalai Lama resided in Tibet before exiling to India in 1959 due to Chinese invasion of Tibet.