Lama, fellow Austrian Hansjörg Auer and American climber Jess Roskelley have been missing in Alberta's Banff National Park since Wednesday. Their sponsor, outdoor apparel company The North Face, said the three members of its Global Athlete Team are presumed dead following an avalanche.
"David dedicated his life to the mountains and his passion for climbing and alpinism shaped and accompanied our family," Claudia and Rinzi Lama said in a statement posted on their son's website. "He always followed his own path and lived his dream. We will accept what now happened as a part of that."
The family expressed gratitude for the support it received "from near and far" and asked that their son be remembered "for his zest for life, his enthusiasm."
Earlier, Austrian Chancellor Sebastian Kurz said Lama and Auer had "shaped the international climbing and alpinist scene in recent years with many achievements."
Lama, 28, was feted for achieving the first free ascent in 2012 of the Compressor Route of the Cerro Torre, one of the most striking peaks in the Andes. The feat was captured in the 2013 documentary "Cerro Torre - A Snowball's Chance in Hell."
The son of a Nepalese mountain guide and an Austrian nurse, Lama had also won numerous climbing competitions in his younger years before devoting himself full-time to mountaineering in 2011.
Auer, 35, became the first person to free solo climb Italy's Marmolada peak via the south face in 2007.
Parks Canada said the three men were attempting to climb the east face of Howse Peak on the Icefields Parkway on Wednesday.
Officials said safety specialists immediately responded by air and observed signs of multiple avalanches and debris containing climbing equipment.
Roskelley climbed Mount Everest in 2003 at age 20. At the time he was the youngest American to climb the world's highest peak.
His father, John Roskelley, told The Spokesman-Review, that the route his son and the other climbers were attempting was first done in 2000.
In the 2013 documentary, Lama addressed the constant peril extreme climbers are exposed to, insisting that the risks were carefully calculated - more like a game of poker than Russian roulette.
"I think it's important to be aware of the risks, but in the end there will always be things that are out of our hands," he said.
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