Howse Peak, the mountain the team was attempting to climb, is an extremely challenging climb.
They were reported missing Wednesday and an investigation into the incident was underway.
Parks Canada is investigating the incident but says unsafe conditions and the risk of further avalanches have prevented any recovery efforts at this time. The forecast for precipitation and strong winds are preventing recovery efforts and will worsen the avalanche risk over the next few days.
Both men reached the summit of Mount Everest together in 2003 and count numerous other alpine achievements.
It is remote and an exceptionally hard objective, with mixed rock and ice routes requiring advanced alpine mountaineering skills.
"I asked him if he wanted to go to Everest, and, of course, he did", said Jess' father and climbing pioneer John Roskelley.
The apparent loss has left the global climbing community devastated as the likelihood they are still alive has slowly diminished.
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.
All three climbers were among the most elite in the world.
Parks Canada described the area as "a remote and an exceptionally hard objective".
"We're looking for a good weather window ... we don't have a timeline", he said.
Google Map view of Howse Peak on the Icefields Parkway.
They were part of a team of experienced athletes sponsored by American outdoor equipment firm The North Face, the company confirmed to AFP.
Roskelley said it's a challenge for only the most extreme climbers.
Parks Canada said the climbers began their ascent on Tuesday and had already climbed various Canadian peaks recently.
At 3,295 metres, Howse Peak is the highest mountain in the Waputik Mountains, a subrange of the Canadian Rockies.
Auer, 35, who grew up near the Dolomites in Austria, guided sheep from the family farm into the mountains every summer as a boy.