[Has there] ever been a team who has not lost a game during the NHL playoffs to win the [Stanley] cup?
Since 1939 (the first best-of-seven Stanley Cup finals), this has taken place only twice, albeit during the era in which there were only six teams in the league (and two playoff rounds).
Between 19261926-1938, this took place five times:
Since 1939 (the first best-of-seven Stanley Cup finals), the following teams lost only once on their way to the Stanley Cup:
† - 12 teams in the league (three playoff rounds)
‡ - 18 teams in the league (three playoff rounds, division winners earned a bye to the quarterfinals)
Between 19261926-1938, the following teams lost only once on their way to the Stanley Cup: