"As we visit His Holiness the Dalai Lama, our bipartisan delegation comes in his spirit of faith and peace. We come on this visit to be inspired by His Holiness and demonstrate our commitment to the Tibetan people, to their faith, their culture and their language," Ms Pelosi said.
The lawmakers' visit comes at a awkward time for Mr Trump. Campaigning for election, he had cast China as a trade adversary and currency manipulator, but he now wants President Xi Jinping's support to restrain nuclear-armed North Korea.
"This is my home," the Dalai Lama said after welcoming the US delegation to his timber-built hilltop residence. He then corrected himself: "This is my second home. My real home — other side."
He then reflected on his fate as a refugee, since fleeing from his homeland in 1959.
"Here, the last 58 years, I am the longest guest of Indian government," the Dalai Lama said. "But, emotionally, some concern about deep inside Tibet, and also in China proper there are 400 million Buddhists."
The Dalai Lama said he would be willing to visit China but this was not possible while Beijing still considered him a "dangerous” separatist.
POLICY ON TIBET
After Mr Trump's election last November, the Dalai Lama said he was keen to meet the incoming US leader. It now looks unlikely the Nobel peace laureate will get a White House invite - an honour accorded by recent American presidents - anytime soon.
Ms Pelosi last visited the Dalai Lama in 2008, in the aftermath of a Chinese crackdown on an uprising in Tibet that coincided with the Beijing Olympics.
The situation in the Tibet Autonomous Region has worsened since then, according to experts and human rights activists, as authorities crackdown on dissent and pursue systematic policies to assimilate Tibetans.
"The level of repression in Tibet has increased tremendously," said Meenakshi Ganguly, South Asia director at Human Rights Watch.
Numbers crossing from Tibet into India and neighbouring Nepal have slowed to a trickle, she added, sapping the vitality of the Tibetan emigre community in South Asia.
Reports continue to emerge from Tibet from time to time of isolated acts of protest against Chinese rule.
A 16-year-old student, chanting "Tibet wants freedom" and "Let His Holiness the Dalai Lama come back to Tibet", burned himself to death on May 2, Radio Free Asia's Tibetan service has reported.
Representative Jim McGovern, a Democrat travelling with Ms Pelosi, has called for a new US policy towards Tibet to safeguard the identity of the Tibetan people and hold China accountable for human rights abuses.
China took control of Tibet in 1950 in what it calls a "peaceful liberation" and has piled pressure on foreign governments to shun the Dalai Lama.