Lauda, not only a F1 legend but also a world-famous aviator, was true to his word after the Chinese grand prix, as the pair returned from Shanghai aboard the great Austrian's Bombardier Global 5000.
"Otherwise, Lewis would have been on a regular flight," the German daily said.
Hamilton's third win of the season also moved him equal to Lauda's career tally of 25 grand prix victories.
Lauda revealed in Shanghai that, last year, he had advised the now on-form Briton to drop his travelling "baggage" of dogs and rap stars.
Indeed, Hamilton is well on track for his second world championship with a permanent travelling entourage of just one -- his trainer.
"This year I'm just able to arrive and drive with no other worries," he confirmed this week.
"It's the combination of lots of things. It's where I am in my life, family, girlfriend, all things: where I live, having the right people in place, management, being in the right team," Hamilton explained.
His teammate Nico Rosberg, however, is still leading the world championship by a few points, which Hamilton admits will be keeping the German's hopes afloat for now.
"In this racing business it's all psychological," said Hamilton.
"Nico's very, very fast but I'm grateful I've been able to put some really good performances in but I owe it to the team. It's incredible what they've done."
Beyond Hamilton versus Rosberg, Mercedes appears to be on a stroll to the 2014 title, notwithstanding the efforts of improving rivals like Red Bull and Ferrari.
"Everything is fine," Lauda agreed, "but there are so many races left.
"The most important will be the next three weeks," he told Spain's EFE news agency, referring to the gap between the initial 'flyaway' phase of the 2014 season and the return to more familiar European soil.
"We'll see who makes the most progress, who is faster and who wins in Barcelona," added Lauda.
"It will be important to see how the rest of the season is going to go. If you're on top in Barcelona, everything will be a little easier," he said.